   Chapter 12.2, Problem 12E ### 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. ∫ 9 x 5 ( 3 x 6 − 4 ) 6   d x

To determine

To calculate: The value of the integral 9x5(3x64)6dx.

Explanation

Given Information:

The provided integral is 9x5(3x64)6dx

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:

9x5(3x64)6dx

Rewrite the integral by multiplying and dividing by 2 as:

1218x5(3x64)6dx

Let u=3x64, then derivative will be,

du=d(3x64)=18x5dx

Substitute du for 18x5dx and u for 3x64 in provided integration.

1218x5(3x64)6dx=12u6du

Now apply, the power formula of integrals:

undu

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