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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Checkpoint 4

Use the integration table in Appendix C to evaluate 0 1 x 2 1 + e x 3 d x .

To determine

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

Explanation

Given Information:

The integral is provided as:

01x21+ex3dx

Formula used:

The formula 39 for integral 11+eudu is:

11+eudu=uln(1+eu)+C

General power differentiation Rule:

ddx[un]=nun1dudx

Calculation:

Consider u=x3.

Differentiate the considered function with respect to x using power rule of differentiation.

du=3x2dx

Consider the provided integral:

01x21+ex3dx

Multiply and divide by 3.

01x21+ex3dx=13013x21+ex3dx=130111+ex33x2dx

Substitute u for x3, and du for 3x2dx

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