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Answers - Calculus 1 Tutor - Worksheet 11 – Integration by Substitution 1. Evaluate the integral using substitution: ∫ t( t + y)5𝑑 Let = t + y and 𝑑 = t𝑑 . Then, 𝑑 =𝑑𝑢 2. Substitute these values into the integral: ∫ t( )5 𝑑 t =∫ 5𝑑 Integrate using the power rule: ∫ 5𝑑 = s x 6+𝐶

On this worksheet you will use substitution, as well as the other integration rules, to evaluate the the given de nite and inde nite integrals. Steps for integration by Substitution 1.Determine u: think parentheses and denominators 2.Find du dx 3.Rearrange du dx until you can make a substitution 4.Make the substitution to obtain an integral in u

Learn how to perform integration by making a substitution with examples and practice exercises. This web-workbook covers linear, trigonometric and inverse trigonometric substitutions.

Math 229 Integration Worksheet – Substitution Method Integrate 1. Z (5x+4)5 dx 2. Z 3t2(t3 +4)5 dt 3. Z p 4x5dx 4. Z t2(t3 +4)1/2 dt 5. Z cos(2x+1)dx 6. Z sin10 xcosxdx 7. Z sinx (cosx)5 dx 8. Z (p x1)2 p x dx 9. Z p

Carry out the following integrations to the answers given, by using substitution only. 1. ( ) 3 2 4 0 243 2 2 3 20 ∫ x x dx− = 2. 2 0 4 1 2 ln3 4 1 2 x dx x = − ∫ + 3. ( ) 1 9 2 3 2 0 2 1 33 ∫x x dx− = 4. ( ) 4 2 0 5 3 12 12ln 9 x dx x = ∫ + 5. ( ) 2 4 1 3569 2 3 1 5 ∫ x x dx− = 6. 6 2 6 272 3 2 9 x dx x = ∫ − 7. 1 2 0 1 ...

AP Calculus BC – Worksheet 41 Integration by u-Substitution Evaluate the indefinite integral by using the given substitution. 1) ³cos 6 ; 6x dx u x 8 2) ³63 9 7 ; 9 7x dx u x 3) ³28 7 ; 7r r dr u r6 7 7 Use substitution to find the indefinite integral. 4) ³12 4 8 2 y y y y dy4 2 3 2 sin 8 9 2 5) 5 53 dx x ³ 6) ³ z dz 7) 14 ln x dx ³ x 8)

MATH 132 Worksheet 5 Integration and Limits Review 1. Determine whether the following integrals converge or diverge. (a) Z 1 1 e x3 dx (b) Z 1 3 1 x 1: dx (c) Z 1 3 1 x0:9 dx (d) Z 1 3 1 p x 2 1 dx (e) 1 p x2 +1 dx (f) Z 1 5 1 (x+4)3=2 dx (g) Z 1 5 1 ( 4)3= dx (h) Z 1 4 x x3 1 dx (i) 1 4 x 3 +1 2. Evaluate the following integrals. (a) Z 1 0 1 p ...

Integration Worksheet - Substitution Method Solutions (a)Let u= 4x 5 (b)Then du= 4 dxor 1 4 du= dx (c)Now substitute Z p 4x 5 dx = Z u 1 4 du = Z 1 4 u1=2 du 1 4 u3=2 2 3 +C = 1

Worksheet 2 - Practice with Integration by Substitution 1. Compute the following integrals. a) Z cos3x dx b) Z 1 3 p 4x+ 7 dx c) Z 2 1 xex2 dx d) R e xsin(e ) dx e) Z e 1 (lnx)3 x f) Z tanx dx (Hint: tanx = sinx cosx) g) Z x x2 + 1 h) Z arcsinx p 1 x2 dx i) Z 1 0 (x2 + 1) p 2x3 + 6x dx 2. Find and correct the mistakes in the following ...

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Calculus Integration by Substitution Worksheet SOLUTIONS Evaluate the following by hand. 1) € 6x2(2x3+1) 5 ... Calculus Integration by Substitution WorksheetSOLUTIONS Author: WilliamsL Created Date: 12/12/2014 3:02:34 PM ...

Integration Worksheet - Substitution Method Solutions (a)Let u= 4x 5 (b)Then du= 4 dxor 1 4 du= dx (c)Now substitute Z p 4x 5 dx = Z u 1 4 du = Z 1 4 u1=2 du 1 4 u3=2 2 3 +C = 1

AP CALCULUS - Integration by Substitution - Free download as PDF File (.pdf), Text File (.txt) or read online for free. This document is a calculus worksheet on integration by substitution with 14 problems. It provides calculus problems where students are asked to evaluate indefinite integrals using substitution. The document contains the problems, spaces for solutions, and an answer key with ...

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Vanier College Calculus II (Commerce) Department of Mathematics 201-203-VA Worksheet: Integration by Substitution 1. Evaluate the following inde nite integrals.

Worksheet - Integration by Substitution Math 142 Page 1 of 9 Find the following integrals 1. Z (5x+4)2 dx Use the substitution u = 5x+4 du = 5dx to obtain Z (5x+4) 2dx = Z u 1 5 du = 1 5 Z u du = 1 5 1 3 u3 +C = 1 15 u3 +C = 1 15 (5x+4)3 +C: 2. Z x3 +2x x2 +1 dx Simplify the fraction by performing long division, x x2 +1 x3 +2x 3x x x obtaining ...

(10:03) ; Math Video Tutorials by James Sousa, Integration by Parts, Additional Examples (7:47) . Review Questions Evaluate the following integrals. (Remark: Integration by parts is not necessarily a requirement to solve the integrals. In some, you may need to use u-substitution along with integration by parts.) 1. 2. 3.

Worksheet - Integration by Substitution Math 142 Page 1 of 4 Find the following integrals 1. Z (5x+4)2 dx Use the substitution u = 5x+4 du = 5dx 2. Z x3 +2x x2 +1 dx Simplify the fraction by performing long division. To solve the second integral use the substitution u = x2 +1 du = 2xdx 3. Z 3t2 t3 +4 5 dt Use the substitution u = t3 +4 du = 3t2 ...

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