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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5.2, Problem 18E
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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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Applying the General Power Rule In Exercises 9-34, find the indefinite integral. Check your result by differentiating. See Examples 1, 2, 3, and 5.

∫ − 12 x 2 ( 1   -   4 x 3 ) 2   d x

To determine

To calculate: The value of the provided indefinite integral ∫−12x2(1−4x3)2dx.

Explanation

Given Information:

The provided indefinite integral is ∫−12x2(1−4x3)2dx.

Formula Used:

According to the general power rule for integration,

If u is a differentiable function of x, then

∫undu=un+1n+1+C,

where n≠−1

and

a−m=1am

Calculation:

Consider the indefinite integral say I,

I=∫−12x2(1−4x3)2dx

Let

1−4x3=u … (1)

Differentiate the above equation with respect to x;

ddx(1−4x3)=dudxddx(1)−ddx(4x3)=dudx(−12x2)=dudx

Or

(−12x2)dx=du … (2)

Substitute the values of 1−4x3 and (−12x2)dx from equations (1) and (2) respectively in the provided integral;

I=

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Sect-5.1 P-1CPSect-5.1 P-2CPSect-5.1 P-3CPSect-5.1 P-4CPSect-5.1 P-5CPSect-5.1 P-6CPSect-5.1 P-7CPSect-5.1 P-8CPSect-5.1 P-1SWUSect-5.1 P-2SWU
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