   Chapter 5.2, Problem 16E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### 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. ∫ 1   -   2 x 2 3 ( − 4 x )   d x

To determine

To calculate: The value of the provided indefinite integral 12x23(4x)dx.

Explanation

Given Information:

The provided indefinite integral is 12x23(4x)dx.

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 n1

Calculation:

Consider the indefinite integral say I,

I=12x23(4x)dx

Above integral can be written in rational exponent form as;

I=(12x2)13(4x)dx

Let

12x2=u … (1)

Differentiate the above equation with respect to x;

ddx(12x2)=dudxddx(1)ddx(2x2)=dudx4x=dudx

Or

(4x)dx=du … (2)

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

I=u

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