   Chapter 12.2, Problem 8E ### 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. ∫ ( 8 x 4 + 5 ) 3 (32 x 3 )  d x

To determine

To calculate: The value of the integral (8x4+5)3(32x3)dx.

Explanation

Given Information:

The provided integral is (8x4+5)3(32x3)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:

(8x4+5)3(32x3)dx

Let u=8x4+5, then derivative will be,

du=d(8x4+5)=32x3dx

Substitute du for 32x3dx and u for 8x4+5 in provided integration.

(8x4+5)3(32x3)dx=u3du

Now apply, the power formula of integrals:

un<

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