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The following integral can be evaluated by using substitution: a) Identify the inside function. = x^3+15x + 15z 3z² + 15 Differentiate: Factorise this: 3x^2+15 = 3 [4 (2²+5) (2³ +152)³ dr X^2+5

The following integral can be evaluated by using substitution: a) Identify the inside function. = x^3+15x + 15z 3z² + 15 Differentiate: Factorise this: 3x^2+15 = 3 [4 (2²+5) (2³ +152)³ dr X^2+5

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.2: Integration By Parts
Problem 35E
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answer part B where i got wrong and part D

d 0 d 3 d O d O d d O d O d O d 8 ū d) Hence write down the indefinite integral: [4 (2²+5) (2³ +152)³ dr (Don't forget the constant of integration as this is an indefinite integral.) Show steps (Your score will not be affected.) 3 Answer: 1/3(x^3+15x)^4+C (x³ + 15z)¹ +c ✔ Evaluate the definite integral, correct to 4 significant figures: Your ans You scor 4 (2²+5) (2³ + 15z)³ dz
Transcribed Image Text:d 0 d 3 d O d O d d O d O d O d 8 ū d) Hence write down the indefinite integral: [4 (2²+5) (2³ +152)³ dr (Don't forget the constant of integration as this is an indefinite integral.) Show steps (Your score will not be affected.) 3 Answer: 1/3(x^3+15x)^4+C (x³ + 15z)¹ +c ✔ Evaluate the definite integral, correct to 4 significant figures: Your ans You scor 4 (2²+5) (2³ + 15z)³ dz
The following integral can be evaluated by using substitution: a) b) Identify the inside function, u = x^3+15x 3 + 15z 3x² + 15 Differentiate: Factorise this: = 3x^2+15 3 X^2+5 Rewrite the whole integral in terms of u and du: f Simplify and cancel z²+5: 4/3 u^3 Integrate with respect to u: 1/3 u^4+c [4 (2²+5) (2³ +152)³ dr +00 4(x^2+5)u^3 du +c x 3 ✓ du X^2+5 > > > > Ga 5 5 9 5 25 25 2 Yc Ga Ga Ga Yc Yc
Transcribed Image Text:The following integral can be evaluated by using substitution: a) b) Identify the inside function, u = x^3+15x 3 + 15z 3x² + 15 Differentiate: Factorise this: = 3x^2+15 3 X^2+5 Rewrite the whole integral in terms of u and du: f Simplify and cancel z²+5: 4/3 u^3 Integrate with respect to u: 1/3 u^4+c [4 (2²+5) (2³ +152)³ dr +00 4(x^2+5)u^3 du +c x 3 ✓ du X^2+5 > > > > Ga 5 5 9 5 25 25 2 Yc Ga Ga Ga Yc Yc
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