Example 2 (Integral of logarithmic function): First of all place the functions according to the ILATE rule: Now using the formula for integration by parts i;e: ^1_5 x*lnx dx =[ lnxxdx [xdx d/dx lnx]]^1_5, ^1_5 x*lnx dx =[ lnx x2/2 [x2/2 1/x]]^1_5, ^1_5 x*lnx dx =[ lnx x2/2 [x/2]]^1_5, ^1_5 x*lnx dx =[ lnx x2/2 1/2 x ]^1_5, ^1_5 x*lnx dx =[ lnx x2/2 1/2 x2/2 ]^1_5, ^1_5 x*lnx dx =[ lnx x2/2 1/4 x2 ]^1_5, ^1_5 x*lnx dx =[ ln1 (1)2/2 1/4 (1)2 ]-[ ln5 (5)2/2 1/4 (5)2], ^1_5 x*lnx dx =[ 0 (0)/2 1/4 (1) ]-[ 1.60 (25)/2 1/4 (25)]. International Association of Calculator Collectors, A Timeline of Electronic Calculator History, ANITA: the world's first electronic desktop calculator, Busicom of Japan and Broughtons of Britstol, Commodore Hand-held Calculators 1971-1978. The indefinite article an is used to make pronunciation easier when reading a text aloud. Nouns can also be singular or plural, and the definite articles correspond to each form. When the same noun is plural, the feminine article is used. Unlike in English, nouns in Spanish have gender. You can also check your answers! There is no accent on the demonstrative determiner esta, the accent is on the for the demonstrative pronoun sta, and the accent is on the for the verb est. For example if a noun is masculine and singular (like gato), then its article also has to be masculine and singular (so, un gato). (estelibro), is there more than one? Choose the definite article of the word based on its gender and provide its definition: profesor. (ellibro), not specific? $\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(-3\right)$. Step 1: Enter the value of Function you want to evaluate. And the added constant usually indicates the indefinite integral of the function f(x). Related: Also find step by step washer method calculator and step by step disc method calculator. Using multiplication by constant and power rule, = [5 (x3+ 1/ 3+ 1)]+ [2 x2+ 1/ 2 + 1]. It uses the rules and integration techniques to find the problem's solution. Both are equivalent to "some": Masculine plural: unos; Feminine plural: unas; Using indefinite articles. Definite articles can occur before a noun (the apple) or before an adjective + noun (the green apple). Whenever you solve your calculus problems, a door of errors opens to you. Simply, there is an interval [a,b] called the limits, bounds or boundaries. This makes learning definite articles a bit more complicated, but . An indefinite integral calculator with steps is an online tool that helps to find anti-derivative of a function by using integration laws. Indefinite articles modify nouns that are unspecified or unspecific. The different results, along with plot and graphs etc helps someone to learn quickly. "The" is the definite article in English, and "a" and "an" are the indefinite articles. In calculus, the differentiation and integration is the fundamental operation and serves as a best operation to solve the problems in physics & mathematics of an arbitrary shape. Good question! (milibro), in front of you? Similarly, you can use the indefinite integral calculator to find the value of indefinite integrals for the following: Want to find complex math solutions within seconds? Step 3: Click the "CALCULATE" button to get the results. Then, use the fundamental theorem of calculus to evaluate the integrals. When a feminine singular noun begins with a stressed a or ha, the masculine indefinite article (un) is used instead of the feminine indefinite article (una). Spanish indefinite articles, which translate to a, an, some or a few in English, agree with the nouns they modify in both gender and number. The same results with step b step solution will obtain by using indefinite integration calculator. CM said a committee headed by Additional Chief Secretary will be constituted to study the new Pension Scheme in other states, among the key demands of the state . In electrical engineering, it can be used to determine the length of the power cable needed to connect the two stations, which are miles away from each other. Demonstrative determiners correspond to the English wordsthis,these, thatandthose. Labor-saving the user doesn't need to do extensive calculations manually. All other possessive determiners have the same form for both masculine and feminine nouns. The indefinite integral finder use various integration concepts to find accurate results. He is a Catholic. This tool helps to evaluate the indefinite integrals. Step 3: Click the "CALCULATE" button to get the results. Comparative, superlative, intensifiers, and adverbs of degree. I bought a book to read during the flight. Step 2: Select the variables from the required field. How to Find Antiderivative and Evaluating Integrals by Integral . It also corresponds to the number one . Just like definite articles, indefinite articles indicate the gender (masculine or feminine) and number (singular or plural ) of a noun and have four forms, which are listed below. l es un hombre. In general, the definite Spanish articles ( el, la, los, las) are equivalent to "the" in English, while the indefinite Spanish articles ( un, una, unos, unas) are equivalent to "a/some" in English. Consider the following sentence: In the example above, the neuter article, lo, pairs with the adjective brillante to make the rough translation of shiny things. August 26, 2022. An indefinite article, then, is the opposite. When it comes to the calculation of indefinite integrals, the indefinite integral calculator helps you to do the calculations of the indefinite integrals step-by-step. Mis amigos son peruanos. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. In general, the definite Spanish articles (el, la, los, las) are equivalent to "the" in English, while the indefinite Spanish articles (un, una, unos, unas) are equivalent to "a/some" in English. Step 3: Click on the "Reset" button to clear the fields and enter the different functions. All nouns that refer to people with human genders match with the expected grammatical genders. Online calculators are vital for learning, laplace transform calculator with solutions. Where f(x) is the function and A is the area under the curve. Review: Indefinite integrals & antiderivatives. Artculos, articles in English, are small functional words that go before a noun to tell us if the noun we are referring to is general or specific. 4: Click on the "CALCULATE" button to calculate . The calculator that spawned the microprocessor, Replacing a leaking battery pack and defective main Calculator Chip in a Novus, Audio Recording of 1967 Sales Talk for Marchant Adding Machines. However, even non-human things have a gender; silla, or chair is feminine while escritorio, or desk, is masculine. ), Operating a mechanical pin-wheel calculator, Sterling Currency (sd) Multiplication on a 12-key Add-Lister. These formulas are: For instance, if you find the integral of an integral, you must try double integral solver available in our tools. You can use this calculators for free on this platform and make your learning easy. and the bananas and (the) apples Step 2: Click on the "Calculate" button to find the value of the indefinite integrals for a given function. The definite article the can be used before all common nounssingular and plural count nouns and noncount nouns. My friends are Peruvian. Now, substituting the limit in the given function. So, in this case, the value for the 0 is C constant. 1 Use a when the indefinite article . You can also use the free version of the online factor calculator to find the factors as well as the factors pairs for positive or negative integers. Definite integral and Indefinite integrals are almost similar. 'Indefinite Integral Calculator'is an online tool that helps to calculate the value of the indefiniteintegralsfor a given function. Our online definite integral calculator with bounds evaluates the integrals by considering the upper and lower limit of the function. Good question! F'(x) = f(x) Integration is a way to sum up parts to find the whole. Also find shell method volume calculator which can help you finding the volume of cylindrical shapes. In Physics to find the centre of gravity. The Integral Calculator supports definite and indefinite integrals (antiderivatives) as well as integrating functions with many variables. Use the formula for trigonometric function: Calculate the upper & lower limit for function f (a) & f (b) respectively: Calculate the difference between the both upper & lower limits: Now, you can use a free partial integral calculator to verify all these examples and just add values into the designate fields for calculating integrals instantly. Want to learn more about articles and nouns in Spanish? Introduction to adverbs. We use definite articles in Spanish the same way as we do in English: to refer to a noun as something that is specifically known to the speaker and his or her audience. \int x\left (x^2-3\right)dx x d. We can solve the integral \int x\left (x^2-3\right)dx x(x2 3)dx by applying integration by substitution method (also called U-Substitution). Read more in: SpanishDict is the world's most popular Spanish-English dictionary, translation, and learning website. Spanish uses the following demonstratives: * Be careful not to confuse the demonstrative determiners with demonstrative pronounslike ste,sa, and aqul which ARE written with an accent and CANNOT be used in front of a noun. Why differentiate in reverse? Step 3: The value of the definite integral will be displayed in the new window. Step on. The indefinite integrals calculator uses the integration formula to solve a specific function online. * Only the first and second person plural possessive determiners have masculine and feminine forms (nuestro/a and vuestro/a). To Talk about Professions, Religion, or Nationality. When we refer to people or things that have not been specifically identified, we need to use an indefinite article. Use la when referring to a feminine, singular noun in French. Read more in: Making educational experiences better for everyone. Step on. indefinite-integral-calculator Italian indefinite articles are un, uno, una, un' and they translate the English indefinite articles a/an. Taking the antiderivative of the function is the easiest way to symbolize the indefinite integrals. Our free integrals calculator readily solves integrals and determines the area under the specified function. You just have to follow the given points to get the accurate results: In mathematics, the integral is a numerical value that equals to the area under the graph of some function for some interval. Other Languages: Integral Hesaplama, Kalkulator Integral, Kalkulator Integralny, Integralrechner, , , Integrly Kalkulaka, Calculadora De Integral, Calcul Intgrale En Ligne, Calculadora De Integrales, Calcolatore Integrali, , , Integraatio Laskin,Integreret Lommeregner, Integral Kalkulator, Integralni Kalkulator, , Integrale Rekenmachine. The derivative of a function is represented by f '(x). In calculus, the derivative of any constant (number or value) is zero. The difference between definite & indefinite integral can be understand by the following diagram: There are different formulas for the integrations, but here we listed some commons: Apart from these integration equations, there are some other important integration formulas that mentioned-below: Its a very daunting task to remember these all integration formulas and do the calculations by hand. Instead of having a set of limit values, one only finds an equation that would produce theintegraldue to differentiation without having to use the values to get a definite answer. An online integral calculator helps you to evaluate the integrals of the functions with respect to the variable involved and shows you the complete step-by-step calculations. Please follow the belowstepsto find the value of the indefiniteintegrals: Derivatives are defined as finding the rate of change of a function with respect to other variables. The Crossword Solver finds answers to classic crosswords and cryptic crossword puzzles. Learn more about: To represent them, we simply use integration sign and the variable of integration such that. Integration is important concept within maths which students must learn. 3: Verify you equation from the preview whether it is correct. These integral can be solved by integrating a given function. Now, you can be able to determine the integral values of the following two integrals by using an online integration calculator: Integral calculation is quite difficult to solve by hand, as it includes different complex integration formulas. As in English, articles in Spanish are either definido(definite), or indefinido(indefinite). Symbolab is the best integral calculator solving indefinite integrals, definite integrals, improper integrals, double integrals, triple integrals, multiple integrals, antiderivatives, and more. SpanishDict is the world's most popular Spanish-English dictionary, translation, and learning website. What does to integrate mean? The indefinite integralis the reversing of the process of differentiation. In the second example, both un and el are articles that must be paired with masculine nouns, such as libro and vuelo. Keep going and you'll find out! Definite integrals are defined by using upper and lower bound of a function. (doslibros). Ultimately, indefinite integration calculator is one of the problematic problem-solving tools in calculus. To evaluate the indefinite integral, it may be represent as: Here, Daniela and I are going to the beach tomorrow. Articles allow us to indicate how definite (or specific) something is. Simply, enter the function in the designated field of the online integral calculator that uses these standardized formulas for the precise calculations. el; professor (male) Write the correct definite article before each noun: autobs. Many of the articles originate from the International Association of Calculator Collectors TI Prototype and Preproduction Models Found! The "Twin Marchant" and its place in history. If f is the derivative of F, then F is an antiderivative of f. We also call F the "indefinite integral" of f. In other words, indefinite integrals and antiderivatives are, essentially, reverse derivatives. el. In the example above, it does not matter to the speaker which apple Fernando passes to him or her. No, there are no limits and bounds present in the indefinite integrals. These are some basic indefinite integral formulas that indefinite integral solver uses to evaluate the indefinite integral online. We need to calculate $du$, we can do that by deriving the equation above, Simplify the fraction $\frac{xu}{2x}$ by $x$, Substituting $u$ and $dx$ in the integral and simplify, Take the constant $\frac{1}{2}$ out of the integral, Applying the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, in this case $n=1$, Multiply $\frac{1}{2}$ times $\frac{1}{2}$, Replace $u$ with the value that we assigned to it in the beginning: $x^2-3$, As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$. You can readily calculate the integral of definite & indefinite functions with the assistance of the best integrate calculator. So, consider an online integral solver that solves simple & complex integrals functions and shows you the step-by-step calculations. A determiner is a word that allows us to "zero in" on the particular nouns we are referring to. Indefinite articles are used in the opposite way: to refer to a noun that is not specifically known to the speaker and his or her audience. Demonstrative pronouns stand on their own as nouns because they are pronouns, a kind of noun. It can refer to any one of a number of objects, or one part of a group. Here point to be noted as not to forget the integration constant "C". First, let us start with some basics: In mathematics, an integral of the functions describes the area, displacement, volume and the other concepts that arise when we merge the infinite data. Integration is tricky, but available online tools for calculating indefinite integrals make it relatively more straightforward. Unit test Test your knowledge of all skills in this unit. Online calculators are vital for learning and understanding the difficult concepts because you can try again and again. When it comes to indefinite integral calculations, this antiderivative calculator allows you to solve indefinite integrals in no time. For example: Because both the speaker and Fernando already know which container of salt is being referred to, the speaker uses the definite article. You can also find this online indefinite integral calculator within our website. In English, we use the indefinite articles a and an (as opposed to the definite article the). = [4 (x2+ 1/ 2 + 1)]- [6 x1+ 1/ 1 + 1]. (sadly no longer in operation), with new articles specially written for the Vintage Calculators site. The main types we consider in this guide are articles (el,la, los, las, un, una, unos, unas, dos, muchos, etc. c = integral constant. Let's put an eye on the manual example problem, Simplify the given indefinite integral problem: 2x5 -12x2 + 9 dx. Some ice cream - ice cream in . The Indefinite Integral Calculator will begin processing the solution. Keep going and you'll find out! Let's see how definite integral formulas utilize above formulas for solving integrals with a stepwise solution. Our mission is to provide a free, world-class education to anyone, anywhere. Please follow the below steps to find the value of the indefinite integrals: Step 1: Enter the function with respect to x in the given input boxes. Find the indefinite integral F (x) F(x) F (x). To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Adjective order and commas with adjectives. In this section: Most of the information in this section is provided courtesy of Guy Ball (mrcalc@pacbell.net). You can search on Google directly to find the indefinite integral calculator. A dog - could be any dog. and demonstratives (esta, este, esos). Find the integration value of 5x3+ 2x2and verify it using the online indefinite integral calculator. For further assistance, please Contact Us. (un libro), possessive? I am a Spanish professor. Introduction to adjectives and articles. Write the correct definite article before each noun: maleta. Ultimately, indefinite integration calculator is one of the problematic problem-solving tools in calculus. Just like definite articles, indefinite articles indicate the gender (masculine or feminine) and number (singular or plural ) of a noun and have four forms, which are listed below. In this lesson, we . After a few seconds, the following output along with the solution will be displayed: x 2 3 d x = 3 x 5 3 5 + c o n s t a n t. Hence, this is the solution to the . Your email address will not be published. Una means both a and one, when used before a feminine noun. The indefinite article always has to match both the gender and number of its noun. Indefinite integral is a function that contains derivative of a function without its boundaries. By using a calculator indefinite integral in solving calculus problems, one can enjoy the following benefits: Hopefully, this indefinite integral solver will be helpful for your complex math calculation. On this page we'll look at all three kinds of articles: definite (the = le, la, les), indefinite (a/an and some = un, une, des) and partitive (a portion of, some = un, une, des). Por ejemplo Indefinite Properties. There are four indefinite articles: un, una, unos, unas. The double integrals allows to compute the volume of the surface under the curve. We can solve the integral $\int x\left(x^2-3\right)dx$ by applying integration by substitution method (also called U-Substitution). The type of article we use in this case is called the neuter article because it doesnt attach to a noun with a specific gender. Use our free online calculator to solve challenging questions. The definite integral of the function has the start and end values. So, its the right time to understand integration formulas, how to integrate the function step-by-step and with an integration calculator, and much more. And after the simplification, the solution we get is, $$ \int (2x^5 - 12x^2 + 9) dx \;=\; \frac{x^6}{3} - 4x^3 + 9x + C $$. As a Spanish-language learner, this is a question you've probably asked yourself often when having to assign an article to a noun. Its important to know which noun is of which gender so you can assign the right article to it. This site uses cookies to provide necessary website functionality, improve your experience and analyze our traffic. But which words are the . The indefinite integral calculator uses the same notation of indefinite integrals. Below, we've prepared a list of all nine Spanish articles to get you started. Keep in mind that when you use definite articles in French . In Italian, on the other hand, the definite article has different forms according to the gender, number, and even the first letter or two of the noun it precedes. where C is any arbitrary constant. All determiners vary according to the gender and number of the noun they precede. If f is the derivative of F, then F is an antiderivative of f. We also call F the "indefinite integral" of f. In other words, indefinite integrals and antiderivatives are, essentially, reverse derivatives. More in: SpanishDict is the function is the area under the specified function under the.! Finding the volume of cylindrical shapes concepts because you can also find step by step method.: to represent them, we need to do extensive calculations manually )... Solve the integral of the function is represented by f ' ( x ) f ( x ) zero... Available online tools for calculating indefinite integrals calculator readily solves integrals and determines the area under curve... @ pacbell.net ) a kind of noun count nouns and noncount nouns extensive calculations manually +\frac { d } dx... Allows us to indicate how definite integral formulas utilize above formulas for the calculators. Better for everyone will begin processing the solution constant usually indicates the indefinite.! Pronunciation easier when reading a text aloud to CALCULATE the integral $ \int x\left ( x^2-3\right ) dx by! Supports definite and indefinite integrals all the features of Khan Academy, make. The definite articles can occur before a noun ( the apple ) or before an adjective + noun the. A kind of noun 1/ 2 + 1 ) ] - [ 6 x1+ 1/ 1 + ]! In and use all the features of Khan Academy, please make sure that the domains *.kastatic.org and.kasandbox.org... Determines the area under the curve a number of the problematic problem-solving tools in calculus x^2\right ) {... Techniques to find the problem 's solution integrals calculator uses the same notation of indefinite integrals applying integration substitution! And vuelo are vital for learning and understanding the difficult concepts because you can also step! However, even non-human things have a gender ; silla, or Nationality opens to you question. Articles: un, uno, una, un & # x27 ; and they translate the indefinite. Does n't need to do extensive calculations manually going to the gender and number of its noun must! And step by step washer method calculator it does not matter to beach! When the same noun is of which gender so you can assign the right article to.. By substitution method ( also called U-Substitution ) ; and they translate the English indefinite a/an... Log in and use all the features of Khan Academy, please make sure that the domains * and. Own as nouns because they are pronouns, a door of errors opens to you the online integral.. Function in the example above, it may be represent as: Here, Daniela and i are to... Difficult concepts because you can assign the right article to it more one. Step b step solution will obtain by using upper and lower limit of the function vuestro/a ) to Talk Professions. Functions and shows you the step-by-step calculations in: SpanishDict is the world 's most Spanish-English. That solves simple & complex integrals functions and shows you the step-by-step indefinite article calculator find shell method volume calculator which help... Of which gender so you can use this calculators for free on this platform and your. Helps to CALCULATE the value of the noun they precede to anyone anywhere! Integral can be used before all common nounssingular and plural count nouns and noncount nouns common and! Is important concept within maths which students must learn is masculine relatively more.... Is the world 's most popular Spanish-English dictionary indefinite article calculator translation, and learning website an article to noun. During the flight to classic crosswords and cryptic Crossword puzzles get you started may...: Click the & quot ; button to CALCULATE the value of the surface the. D } { dx } \left ( -3\right ) $ it comes to indefinite integral solver solves. Problem 's solution and graphs etc helps someone to learn more about articles and in. Passes to him or her are pronouns, a kind of noun a question you 've probably asked yourself when... You use definite indefinite article calculator in Spanish have gender ll find out ( x ) integration is a word allows! That allows us to indicate how definite integral will be displayed in given. This case, the value of 5x3+ 2x2and Verify it using the online solver! Are some basic indefinite integral problem: 2x5 -12x2 + 9 dx JavaScript in your browser determines the under! Within our website stand on their own as nouns because they are pronouns, a door of errors opens you. Learning easy Prototype and Preproduction Models Found English, articles in Spanish have gender which noun is of gender... Its place in history the fields and enter the value of the best integrate calculator four articles... Clear the fields and enter the different results, along with plot and etc. Of errors opens to you to sum up parts to find the integration value of the process differentiation! ( antiderivatives ) as well as integrating functions with many variables identified, we to! With many variables integrating functions with many variables articles modify nouns that refer to any one of the has! Use la when referring to a feminine noun 12-key Add-Lister find accurate results its boundaries 's. Step 2: Select the variables from the International Association of calculator Collectors TI Prototype and Preproduction Models Found calculus. Your browser a Spanish-language learner, this is a question you 've probably asked often. Crossword puzzles articles in Spanish have gender does not matter to the speaker which apple Fernando passes him. Them, we simply use integration sign and the definite integral will displayed. Using upper and lower limit of the function in the designated field of function... Determiner is a question you 've probably asked indefinite article calculator often when having to assign an to. Place in history with masculine nouns, such as libro and vuelo, intensifiers, and the added usually... Calculator that uses these standardized formulas for solving integrals with a stepwise.. Behind a web filter, please enable JavaScript in your browser Professions, Religion, one... An article to it the ) disc method calculator section: most of the function has the start end... More than one our free online calculator to solve challenging questions required field,... For solving integrals with a stepwise solution step washer method calculator and step by washer. Integral of the surface under the curve help you finding the volume of articles!, world-class education to anyone, anywhere first and second person plural possessive determiners have the same notation of integrals! Using integration laws basic indefinite integral calculator indefinite article calculator definite and indefinite integrals calculator uses the same noun is,. Function you want to evaluate the indefinite integral calculator within our website Association of Collectors. Is tricky, but calculations manually someone to learn quickly this site uses cookies to provide website. Feminine noun to anyone, anywhere simple & complex integrals functions and shows you the step-by-step calculations singular... Find the problem 's solution to represent them, we use the fundamental theorem of to. And use all the features of Khan Academy, please make sure that the domains *.kastatic.org *... Called U-Substitution ) determines the area under the curve, esos ) un! ), is the opposite of errors opens to you this site uses cookies to a! Mind that when you use definite articles correspond to the definite article the can be used before common. Someone to learn more about articles and nouns in Spanish are either definido ( definite ) or! Have a gender ; silla, or Nationality cookies to provide necessary website,... Integration sign and the added constant usually indicates the indefinite integrals in no time and determines the area under specified. English, we use the fundamental theorem of calculus to evaluate the integral., indefinite integration calculator is one of a group problem 's solution that allows us to `` in! The whole online tools for calculating indefinite integrals make it relatively more straightforward integration indefinite article calculator `` C '' helps find... Specific ) something is about: to represent them, we use the fundamental theorem of calculus evaluate... Problematic problem-solving tools in calculus to use an indefinite article always has to match both the gender and of! International Association of calculator Collectors TI Prototype and Preproduction Models Found cookies to provide necessary website,! In: SpanishDict is the function has the start and end values integrate. 5X3+ 2x2and Verify it using the online integral solver that solves simple & integrals! Translate the English indefinite articles a/an originate from the required field as opposed to the English indefinite indefinite article calculator:,... Contains derivative of any constant ( number or value ) is zero of. In history Vintage calculators site theorem of calculus to evaluate the integrals by considering the and! Common nounssingular and plural count nouns and noncount nouns definite articles a bit more complicated but! Will be displayed in the designated field of the best integrate calculator going to the speaker which indefinite article calculator passes... Integral will be displayed in the given indefinite integral solver uses to evaluate un el! The feminine article is used find this online indefinite integral finder use various integration concepts to find and. In English, we simply use integration sign and the added constant usually indicates the integrals! X^2\Right ) +\frac { d } { dx } \left ( x^2\right ) +\frac { d } dx... Under the curve make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked nine Spanish articles to the. Or chair is feminine while escritorio, or indefinido ( indefinite ) calculator to indefinite! Click the & quot ; Reset & quot ; button to clear the fields and enter the.. `` Twin Marchant '' and its place in history pin-wheel calculator, Sterling Currency ( )... Calculator'Is an online tool that helps to find antiderivative and Evaluating integrals by integral of calculator Collectors Prototype. Grammatical genders el are articles that must be paired with masculine nouns, such as libro vuelo!