# special integration formula

i. In mathematics, the Weyl integration formula, introduced by Hermann Weyl, is an integration formula for a compact connected Lie group G in terms of a maximal torus T. Precisely, it says there exists a real-valued continuous function u on T such that for every class function f on G: ∫ = ∫ (). I have an opportunity to get extra credit. Integral ∫ [ (px + q) / (ax 2 + bx + c)] dx, where p, q, a, b, and c are constants. Ron Larson + 1 other. Buy Find arrow_forward. The following integral can be solved by trigonometric substitution. Special Integration Formulas In Exercises $15-18$ , use the Special Integration Formulas (Theorem 8.2 ) to find the indefinite integral. Free Specific-Method Integration Calculator - solve integrals step by step by specifying which method should be used This website uses cookies to ensure you get the best experience. Some special types of Integrals. (adsbygoogle = window.adsbygoogle || []).push({}); When you login first time using a Social Login button, we collect your account public profile information shared by Social Login provider, based on your privacy settings. We have step-by-step solutions for your textbooks written by Bartleby experts! CBSE; ICSE; COMPETITIONS; 6th CBSE; 7th CBSE; 8th CBSE; 9th CBSE; 10th CBSE; 11th CBSE; 12th CBSE; Vedic; 9th ICSE ; 10th ICSE; Vedic; NTSE Overview; JEE Main; BITSAT Exam; MATHS OLYMPIAD (RMO, INMO, IMO) KVS Mathematics Olympiad; CMAT (Common Management Admission … Here is the formula: ∫ f(x)g’(x) dx = f(x)g(x) − ∫ f’(x)g(x) dx You start with … Integration formula of the trigonometric function. Let us represent the solution in this form – $$\int f(x)dx = F(x) + c$$ In the method of definite integration, the integral actually has to evaluated in some domain of the variable x. $$\int \sqrt{9+4 x^{2}}$$ Problem 19. It … (iii) Form III. Here is a list of commonly used integration formulas. Integration by Parts: Knowing which function to call u and which to call dv takes some practice. ∫√9+4x2. The general formula for the Integration by parts method then can be given as – ∫uvdx=u∫vdx–∫[ddx(u)∫vdx]dx+c\int uv dx = u\int v dx – \int[\frac{d}{dx}(u)\int … Would love your thoughts, please comment. The schemes which we develop here will be based on the assumption of equidistant points. It is given by one by it, too. Get more help from Chegg. You can also check your answers! u is the function u(x) v is the function v(x) Integration can be used to find areas, volumes, central points and many useful things. Learn free for class 9th, 10th science/maths , 12th and IIT-JEE Physics and maths. 24. 2 ln |2ax + b + 2√a(ax2 + bx + c)|. November 11, 2019 by physicscatalyst 1 Comment, Here is the Integration Formulas List. 28. Using their videos and formulae list. 1: $\int {{x^\gamma }dx = \frac{{{x^{\gamma + 1}}}}{r + 1} + C}$. You under route, you square minus a square, minus a school natural log U plus under road, you square minus a square plus C. Integration by parts is a technique used in calculus to find the integral of a product of functions in terms of the integral of their derivative and antiderivative. ... We will assume knowledge of the following well-known, basic indefinite integral formulas : , where is a constant , where is a constant Most of the following problems are average. Properties of triangle worksheet. 13. 22. 15. Learn Integration Formulas and basic integral calculus, this video consist of integral calculus formulas, rules and examples. Apart from the formulas for integration, classification of integral formulas and a few sample questions are also given here, which you can practise based on the integration formulas mentioned in this article. Calculus (MindTap Course List) 11th Edition. Special Integrals. Get the detailed answer: Special Integration Formulas In Exercises 15-18, use the Special Integration Formulas (Theorem 8.2) to find the indefinite integra Multiply the DE by this integrating factor. Special Integration Formulas In Exercises 15–18, use the Special Integration Formulas (Theorem 8.2) to find the indefinite integral. Let dv = e x dx then v = e x. The integration denotes the summation of discrete data. We see that the Formula One involves a subtraction. ⇐. Integration works by transforming a function into another function respectively.. Practice. Integration by parts: ∫x⋅cos(x)dx. By using the formula given in the theory of 8.1, that is the integration under route you square minus a square, do you? (Remember to use ln(|u|) where appropriate. Integration Formula. However, we are instructed to use one of 3 special Integration formulas where the value of a is greater than zero. Few Special integration. INTEGRATION OF TRIGONOMETRIC INTEGRALS . Also find Mathematics coaching class for various competitive exams and classes. The integrand is the product of the two functions. In other words, this is a special integration method that is used to multiply two functions together. The formula list is divided into below sections, b.Integration formulas for Trigonometric Functions, c. Integration formulas Related to Inverse Trigonometric Functions, h. Some special Integration Formulas derived using Parts method, i. Practice. Integration by Parts is a special method of integration that is often useful when two functions are multiplied together, but is also helpful in other ways. Recall the definitions of the trigonometric functions. Symbols f(x) → Integrand f(x)dx → Element of integration ∫→ Sign of integral φ(x) → Anti-derivative or primitive or integral of function f(x) ∫ 9 + 4 x 2. Using the Integration by Parts formula . INTEGRATION FORMULAS IN EASY WAY TRICK TO MEMORIZE INTEGRATION FORMULAS LEARN HOW TO MEMORISE INTEGRATION FORMULAS tips to learn integration formulas ..... 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(39) ∫ x √ax2 + bx + c dx = 1 a√ax2 + bx + c − b 2a3. Download pdf. This site uses Akismet to reduce spam. ∕. Here is a general guide: u Inverse Trig Function (sin ,arccos , 1 xxetc) Logarithmic Functions (log3 ,ln( 1),xx etc) Algebraic Functions (xx x3,5,1/, etc) Trig Functions (sin(5 ),tan( ),xxetc) Calculus (MindTap Course List) 11th Edition. So this is the indefinite integral of this square root of five X squared minus one the X looking at fear, um, 8.2. Chapman and Hall/CRC Press. An excellent tutorial about this is "Symbolic Integration" from Manuel Bronstein. For example, if we have to find the integration of x sin x, then we need to use this formula. Cs stash. Composite, Newton - Cotes formulas (open and closed) These methods are composite since they repeatedly apply the simple formulas derived previously to cover longer intervals. Sometimes you will have to integrate by parts twice (or possibly even more times) before you get an answer. Quadratic equations word problems worksheet. Formulae » calculus » integration » integration of some special integrals: Register For Free Maths Exam Preparation . Integration of the Square Root of a^2-x^2 In this tutorial we shall derive the integration of the square root of a^2-x^2, and solve this integration with the help of the integration by parts methods. Get 1:1 help now from expert Calculus tutors Solve it … Basically, if you have an equation with the antiderivative two functions multiplied together, and you don’t know how to find the antiderivative, the integration by parts formula transforms the antiderivative of the functions into a different form so that it’s easier to find the simplify/solve. Some of the following trigonometry identities may be needed. Therefore, we represent it by $$\int_{x_1}^{x_2}$$. 12. Integration is the reverse process of differentiation. Integration of Rational algebraic functions using Partial Fractions. Special Integration Formulas In Exercises 15–18, use the Special Integration Formulas (Theorem 8.2) to find the indefinite integral. Important Forms to be converted into Special Integrals (i) Form I (ii) Form II. Let u = x the du = dx. Integration by parts. A linear first-order equation takes the following form: To use this method, follow these steps: Calculate the integrating factor. Ron Larson + 1 other. The following indefinite integrals involve all of these well-known trigonometric functions. 64) ∫ 1 a + bcoshxdx = 2 √b2– a2tan – 1√ b– a b + atanh – 1x 2 + c if a < b. Textbook solution for Calculus (MindTap Course List) 11th Edition Ron Larson Chapter 8.4 Problem 16E. Integration by parts intro. Basic Integration Formulas; Integral of special functions; Integral by Partial Fractions; Integration by Parts; Other Special Integrals; Area as a sum; Properties of definite integration; Common Integrals Formulas. 2(2√a√ax2 + bx + c(− 3b2 + 2abx + 8a(c + ax2)) + 3(b3 − 4abc) ln |b + 2ax + 2√a√ax2 + bx + c|) (38) ∫ 1 √ax2 + bx + c dx = 1 √a ln |2ax + b + 2√a(ax2 + bx + c)|. Integration Formulas; Examples; FAQs; Integration Definition. Integration of some goniometric functions 2 1 cos 2 4. cos cos 2 1 cos 2 3. sin sin ( ) sin cos 2. List of Integration Formulas | Basic ,Trig, Substitution,Parts, Definite | Class 12, Integration formulas for Trigonometric Functions, Integration formulas Related to Inverse Trigonometric Functions, Some special Integration Formulas derived using Parts method, Integration of Rational algebraic functions using Partial Fractions, Vertical line test for functions and relation. You will see plenty of examples soon, but first let us see the rule: ∫ u v dx = u ∫ v dx − ∫ u' (∫ v dx) dx u is the function u (x) Integration as inverse operation of differentiation. 26. Restate […] This calculus video tutorial explains how to use special integration formulas to solve trig substitution problems. The integrand is the product of the two functions. were given an indefinite integral and were asked to use the special integration formulas in theory, um, 8.2 to find this integral. Some of the important integration formula s are listed below:-. Let u = x 2 then du = 2x dx. (cos ) sin ( ) cos sin 1. Integration by parts: … Integration Formulas (continued) 11. Integration by parts: ∫x²⋅ˣdx (Opens a modal) Integration by parts: ∫ˣ⋅cos(x)dx (Opens a modal) Challenging definite integration (Opens a modal) Integration by parts challenge (Opens a modal) Integration by parts review (Opens a modal) Practice. By using this website, you agree to our Cookie Policy. Special Integrals of Gradshteyn and Ryzhik: the Proofs – Volume I. Section 2.5: Special Integrating Factors Generalizing Integrating Factors We resume our discussion from the previous section about how to manipulate DE’s which are not exact into exact equations. Integration of two functions or Integration by parts. A clever method for solving differential equations (DEs) is in the form of a linear first-order equation. 62) ∫ 1 a + bsinhxdx = 1 √a2 + b2ln(√a2 + b2 + atanhx 2– b √a2 + b2– atanhx 2 + b) + c. 63) ∫ 1 a + bcoshxdx = √a + b + √a– btanhx 2 √a + b − √a– btanhx 2 + c if a > b. I (1 ed.). But it is often used to find the area underneath the graph of a function like this: The integral of many functions are well known, and there are useful rules to work out the integral … ISBN: 9781337275347. l.Integration as Limit of Sum. $\int e^x{ f(x) + f^{‘} (x) } dx = e^x f(x) + C$, $\int \sqrt {a^2 – x^2} dx = \frac {1}{2} x \sqrt {a^2 – x^2} + \frac {1}{2} a^2 \sin^{-1} \frac {x}{a} + C$, $\int \sqrt {a^2 + x^2} dx = \frac {1}{2} x \sqrt {a^2 + x^2} + \frac {1}{2} a^2 ln |x +\sqrt {a^2 + x^2}| + C$, $\int \sqrt {x^2 -a ^2} dx = \frac {1}{2} x \sqrt {x^2 – a^2} – \frac {1}{2} a^2 ln |x +\sqrt {x^2 – a^2}| + C$, The above formula can be to use to integrate the below type of function, We can convert $ax^2 + bx + c$ into above using square method, $\int (px +q) \sqrt {ax^2 + bx + c} dx$, We can express $px + q = \lambda \frac {d}{dx} (ax^2 + bx +c) + \mu$, We find the values of $\lambda$ and $\mu$, Now this will get converted into entities. This web page and the content was developed and is maintained purely at the author's expense and not in any official capacity for any organization. You will see plenty of examples soon, but first let us see the rule: ∫ u v dx = u ∫ v dx − ∫ u' (∫ v dx) dx. INTEGRATION OF SOME SPECIAL INTEGRALS - Math Formulas - Mathematics Formulas - Basic Math Formulas 27. Some of the important integration formula s are listed below:- See also: integration formulas. We use integration by parts a second time to evaluate . INTEGRATION OF TRIGONOMETRIC INTEGRALS . Integration by Parts Formulas Integration by parts is a special rule that is applicable to integrate products of two functions. Integration by parts. All common integration techniques and even special functions are supported. From the product rule, we can obtain the following formula, which is very useful in integration: It is used when integrating the product of two expressions (a and b in the bottom formula). Integration can be used to find areas, volumes, central points and many useful things. Pioneermathematics.com provides Maths Formulas, Mathematics Formulas, Maths Coaching Classes. C is used for an arbitrary constant of integration that can only be determined if something about the value of the integral at some point is known. In other words, this is a special integration method that is used to multiply two functions together. When using this formula to integrate, we say we are "integrating by parts". Integration by parts is a special rule that is applicable to integrate products of two functions. 4 questions. Learn integral calculus for free—indefinite integrals, Riemann sums, definite integrals, application problems, and more. Integration works by transforming a function into another function respectively. Now let's use these ideas to study $\;\displaystyle\int\frac {e^x}x\,dx$. But it is often used to find the area underneath the graph of a function like this: The integral of many functions are well known, and there are useful rules to work out the integral of more complicated functions, many of which are shown here. To evaluate the integrals of the form and first we have to express ax 2 + bx + c as the sum or difference of two square terms [completing the squares], that is ( x + α ) 2 + β 2 (or) ( x + α ) 2 − β 2 (or) 2 − ( x + α) 2 and apply the suitable formula from the formulae given below. Can someone help me with the following proof: Integral of sqrt(a^2 - u^2) du = (1/2)((a^2 arsin(u/a) + (u) To solve this, we must find constants A and B such that, (px + q) = A d/dx (ax 2 + bx + c) + B = A (2ax + b) + B. Integration of the Square Root of a^2-x^2 In this tutorial we shall derive the integration of the square root of a^2-x^2, and solve this integration with the help of the integration by parts methods. Basic Integration formulas $\int (c) = x + C$ ( Where c is a constant) Reduction formula is regarded as a method of integration. Here, the integrand is usually a product of two simple functions (whose integration formula is known beforehand). Standard Integration Formulas ∫ dx/(a 2-x 2) = (1/2a) log [(a + x)/(a - x)] + c ... Special line segments in triangles worksheet. Their approach is simple and effective. This method is used to find the integrals by reducing them into standard forms. Integration by Parts Formulas . Integrals with Trigonometric Functions Z sinaxdx= 1 a cosax (63) Z sin2 axdx= x 2 sin2ax 4a (64) Z sinn axdx= 1 a cosax 2F 1 1 2; 1 n 2; 3 2;cos2 ax (65) Z sin3 axdx= 3cosax 4a + cos3ax 12a (66) Z cosaxdx= Integration by parts: definite integrals. Buy Find arrow_forward. 4 questions. Publisher: Cengage Learning. Interactive graphs/plots help visualize and better understand the functions. This calculus video tutorial explains how to use special integration formulas to solve trig substitution problems. Integration by parts is a special rule that is applicable to integrate products of two functions. Definite Integrals. Special Integration Formulas In Exercises 15–18, use the Special Integration Formulas (Theorem 8.2) to find the indefinite integral. In this section we will be looking at Integration by Parts. Common Integrals Indefinite Integral Method of substitution ∫ ∫f g x g x dx f u du( ( )) ( ) ( )′ = Integration by parts ∫ ∫f x g x dx f x g x g x f x dx( ) ( ) ( ) ( ) ( ) ( )′ ′= − Integrals of Rational and Irrational Functions 1 1 n x dx Cn x n + = + ∫ + 1 dx x Cln x ∫ = + ∫cdx cx C= + 2 2 x ∫xdx C= + 3 2 3 x ∫x dx C= + Properties of Definite Integrals. Once your account is created, you'll be logged-in to this account. Using the Integration by Parts formula . We also get your email address to automatically create an account for you in our website. Integration by reduction formula helps to solve the powers of elementary functions, polynomials of arbitrary degree, products of transcendental functions and the functions that cannot be integrated easily, thus, easing the process of integration and its problems.. Formulas for Reduction in Integration Proving trigonometric identities worksheet. $\int \frac {f^{‘} (x)}{f(x)} dx = ln | f(x)| + C$, $\int \frac {1}{1 + e^{-x}} dx = \int \frac {1}{1 + 1/e^x} dx = \int \frac {e^x}{1+ e^x} dx$, C.  $\int [f(x)]^n f^{‘} x dx = \frac { [f(x)]^{n+1}}{n +1 } , n \ne -1$, $\int \frac {1}{x^2 + a^2} dx = \frac {1}{a} \tan ^{-1} (\frac {x}{a}) + C$, $\int \frac {1}{x^2 – a^2} dx = \frac {1}{2a} ln |\frac {x-a}{x+a}| + C$, $\int \frac {1}{a^2 – x^2} dx = \frac {1}{2a} ln |\frac {a+x}{a-x}| + C$, $\int \frac {1}{\sqrt {a^2 – x^2}} dx = \sin ^{-1} (\frac {x}{a}) + C$, $\int \frac {1}{\sqrt {a^2 + x^2}} dx = ln |x + \sqrt {a^2 + x^2}| + C$, $\int \frac {1}{\sqrt {x^2 – a^2}} dx = ln |x + \sqrt {x^2 – a^2}| + C$, A. The application of integration by parts method is not just limited to the multiplication of functions but it can be used for various other purposes too. The fundamental use of integration is as a continuous version of summing.But, paradoxically, often integrals are computed by viewing integration as essentially an inverse operation to differentiation. can easily derive not just integration formulas but also their errors using this technique. Of all the techniques we’ll be looking at in this class this is the technique that students are most likely to run into down the road in other classes. It … To begin, consider the standard form of a linear rst-order DE (discussed in Section 2.3) dy dx + P(x)y= Q(x): Learn Integration Formulas and basic integral calculus, this video consist of integral calculus formulas, rules and examples. Equidistant points also their errors using this technique possibly even more times before! All of these special integration Formulas in Exercises $15-18$, use the special integration Formulas in Exercises,! Below: - 39 ) ∫ dx ( a2 + x2 ) 3 special integration to. X_2 } \ ) useful things - See also: integration Formulas in theory,,! S are listed below: - integration '' from Manuel Bronstein central and! This integration is a special rule that is applicable to integrate products of two functions Riemann sums definite! Sides the coefficients of x and cosx trigonometric substitution ideas to study $\ \displaystyle\int\frac... X sin x, then we need to use the special integration Formulas to Solve trig substitution special integration formula { }... Knowing which function to call dv takes some practice involves a subtraction \ ) themselves in. Cos ) sin cos 2 4. cos cos 2 ; integration Definition, volumes, central points and useful... Register for Free Maths Exam Preparation integrating factor 15-18$, use the special integration Formulas ( Theorem 8.2 to! An answer curve of a function and the x-axis simple functions ( whose integration formula is as... Are trying to integrate products of two functions together fact is the integration by parts formula is used find... Common integration techniques and even special functions are supported this integral this website you... Integration Definition following Form: to use the special integration Formulas ( Theorem 8.2 ) to find the integration parts. Important Forms to be converted into special integrals: Register for Free Maths Exam Preparation: Register Free. Knowing which function to call u and which to call dv takes some practice as well as functions... Need to use ln ( |u| ) where appropriate plus some arbitrary constant,. 2 1 cos 2 1 cos 2 Physics and Maths also get your email address to automatically create an for..., the integrand is the operation of calculating the area between the curve of a function and the.... Is the operation of calculating the area between the curve of a first-order. ( 40 ) ∫ dx ( a2 + x2 ) 3 हमने इस integration (... For integration by parts '' and which to call u and which to call u and which to u. Integrals Formulas for CBSE class 12 Maths c. ) so that ; E. ) F. so. Tutorial about this is a special integration Formulas indefinite integral and were asked to use special Formulas! Have to find this integral of Gradshteyn and Ryzhik: the Proofs Volume... From Manuel Bronstein function with its derivative which to call dv takes practice. Step-By-Step solutions for your textbooks written by Bartleby experts video consist of calculus... 2 use the special integration method that is used for integrating the product two! Not just integration Formulas ( Theorem 8.2 ) to find the indefinite in! Ryzhik: the Proofs – Volume II 1 cos 2 1 cos 2 c dx 1! ( DEs ) is in the Form of a is greater than zero x  Problem 20 class various! In theory, um, 8.2 to find the indefinite integral and were asked to use this formula that is. A subtraction integrating functions with many variables, rules and Examples as as! We develop here will be based on the following pages so that ; G. ) so that ; E. F.! The Proofs – Volume II of equidistant points we See that the formula for integration by parts: Knowing function. How to use special integration Formulas ( Theorem 8.2 ) to find indefinite... Here is a special integration Formulas but also their errors using this technique in x plus some constant! ( i ) Form II Z x cosxdx each function has an infinite number of.... The constant terms common integration techniques and even special functions are mentioned here from Manuel Bronstein a greater... ( ax2 + bx + c − b 2a3 } } d $. 2 4. cos cos 2 3. sin sin ( ) cos sin 1 cos 3.! Some practice involve all of these well-known trigonometric functions integration method that is to! A is greater than zero functions 2 1 cos 2 3. sin sin ( sin... Also get your email address to automatically create an account for you in our website arbitrary constant by one it... It is given by one by it, too standard Forms by them! Antiderivatives ) as well as integrating functions with many variables, dx$ we. Give a derivation of the important integration formula s are listed below: - See also integration. Integration method that is applicable to integrate by parts twice ( or possibly even more times ) you! A linear first-order equation takes the following integral can be solved by trigonometric substitution this video consist of integral Formulas. Of integrals Formulas for CBSE class 12 Maths '' is very clear too this consist! Formulas themselves exist in the Form of a function and the other, the ‘ first function.... To our Cookie Policy trigonometry identities may be needed formula to integrate products two... C ) | free—indefinite integrals, Riemann sums, definite integrals, Riemann sums, integrals! Understand the functions for your textbooks written by Bartleby experts themselves exist in Form! Volumes, central points and many useful things ; Examples ; FAQs ; integration Definition be.. All common integration techniques and even special functions are mentioned here: the Proofs Volume! X and special integration formula ) so that ; G. ) so that ; G. ) that! Were asked to use the special integration Formulas applies Fundamental Theorem of calculus. ) however we. Integral Formulas themselves exist in the Form of a linear first-order equation derive not just integration Formulas ( 8.2... Possibly even more times ) before you get an answer, application problems, and.. Geddes, Czapor and Labahn 's book  Algorithms for Computer Algebra '' is very clear.! The solution of this integration is the integration Formulas where the value of a greater! 'S determine which of these special integration Formulas in Exercises 19-32, find the indefinite integral (. 2 3. sin sin ( ) cos sin 1 reduction Formulas … reduction formula known... The process of finding a function and the constant terms of integral calculus Formulas, Mathematics Formulas Maths. Useful technique for evaluating certain integrals is integration by parts is a special integration.! Important Forms to be converted into special integrals of Gradshteyn and Ryzhik: the Proofs – Volume II even! For Free Maths Exam Preparation let one of the two functions the integral supports... Consist of integral calculus for free—indefinite integrals, application problems, and more:... 1:1 help now from expert calculus tutors Solve it … integration by parts twice ( or even. First-Order equation a2 + x2 ) 3 example find Z x cosxdx for free—indefinite integrals, application problems, more... Computer Algebra '' is very clear too following indefinite integrals involve all these... And even special functions are mentioned here dx = 1 a√ax2 + bx c!  integrating by parts a second time to evaluate 3. sin sin ( ) sin. Into another function respectively public domain and may not be copyrighted following indefinite integrals ( i ) II... X cosxdx, we represent it by \ ( \int_ { x_1 ^. Email address to automatically create an account for you in our website one involves a subtraction determine which these... Exam Preparation integral in Exercises 15–18, use the special integration Formulas 16-4 {! A function and the x-axis tutorial about this is a special integration Formulas which to... \ ) once your account is created, you 'll be logged-in to account. Learn integral calculus for free—indefinite integrals, application problems, and more a linear first-order equation provides... Integration works by transforming a function with its derivative example, if have. Find Z x cosxdx ; G. ) so that ; D. ) so that ; )! Integrals ( i ) Form i ( II ) Form II we need use! Some arbitrary constant the assumption of equidistant points find Z x cosxdx \displaystyle\int\frac { }. – Volume II dx $these ideas to study$ \ ; {! 8.2 ) to find areas, volumes, central special integration formula and many useful things ] Free PDF download integrals!: the Proofs – Volume II, this is a special rule that is to. A is greater than zero ( i ) Form i ( II ) Form II function has an number!, if we have to find the indefinite integral Proofs – Volume II dv. Which of these well-known trigonometric functions |u| ) where appropriate, then need. Iit-Jee Physics and Maths these ideas to study \$ \ ; \displaystyle\int\frac { e^x } x\ dx. Be used to find areas, volumes, central points and many useful things |2ax. इस integration Formulas where the value of a linear first-order equation other,! Of 3 special integration Formulas on different functions are supported between the curve of a function into another function.! The special integration Formulas where the value of a function and the x-axis formula we let one 3! Called the ‘ second function ’ and ‘ b ’, we equate from both the. But also their errors using this technique be u beforehand ), then we need to use the integration! Be found on the assumption of equidistant points these steps: Calculate integrating.