Explanation Given Information: The integral is provided as: ∫ 0 1 x 2 1 + e x 3 d x Formula used: The formula 39 for integral ∫ 1 1 + e u d u is: ∫ 1 1 + e u d u = u − ln ( 1 + e u ) + C General power differentiation Rule: d d x [ u n ] = n u n − 1 d u d x Calculation: Consider u = x 3 . Differentiate the considered function with respect to x using power rule of differentiation. d u = 3 x 2 d x Consider the provided integral: ∫ 0 1 x 2 1 + e x 3 d x Multiply and divide by 3 . ∫ 0 1 x 2 1 + e x 3 d x = 1 3 ∫ 0 1 3 x 2 1 + e x 3 d x = 1 3 ∫ 0 1 1 1 + e x 3 3 x 2 d x Substitute u for x 3 , and d u for 3 x 2 d x

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 6.2, Problem 4CP

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To calculate: The value of definite integral ∫01x21+ex3dx.

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Chapter 6.2, Problem 3CP

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Chapter 6 Solutions

Calculus: An Applied Approach (MindTap Course List)

Ch. 6.1 - Prob. 1CP Ch. 6.1 - Prob. 2CP Ch. 6.1 - Prob. 3CP Ch. 6.1 - Prob. 4CP Ch. 6.1 - Prob. 5CP Ch. 6.1 - Prob. 6CP Ch. 6.1 - Prob. 7CP Ch. 6.1 - Prob. 1SWU Ch. 6.1 - Prob. 2SWU Ch. 6.1 - Prob. 3SWU

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The value of definite integral ∫ 0 1 x 2 1 + e x 3 d x .

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To calculate: The value of definite integral ∫01x21+ex3dx.

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Chapter 6 Solutions