   Chapter 12.2, Problem 9E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Evaluate the integrals in Problems 7-36. Check your results by differentiation. ∫ ( 3 x − x 3 ) 2 (3 − 3 x 2 )  d x

To determine

To calculate: The value of the integral (3xx3)2(33x2)dx.

Explanation

Given Information:

The provided integral is (3xx3)2(33x2)dx

Formula used:

The power formula of integrals:

undu=un+1n+1+C (forn1)

The power rule of differentiation:

ddu(un)=nun1

Calculation:

Consider the provided integral:

(3xx3)2(33x2)dx

Let u=3xx3, then derivative will be,

du=d(3xx3)=(33x2)dx

Substitute du for (33x2)dx and u for 3xx3 in provided integration.

(3xx3)2(33x2)dx=u2du

Now apply, the power formula of integrals:

und</

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