   Chapter 12.2, Problem 16E ### 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. ∫ 5 x 3 ( 3 x 4 + 7 ) − 4 d x

To determine

To calculate: The value of the integral 5x3(3x4+7)4dx.

Explanation

Given Information:

The provided integral is 5x3(3x4+7)4dx

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:

5x3(3x4+7)4dx

Rewrite the integral by multiplying and dividing by 12 as:

51212x3(3x4+7)4dx

Let u=3x4+7, then derivative will be,

du=d(3x4+7)=12x3dx

Substitute du for 12x3dx and u for 3x4+7 in provided integration.

51212x3(3x4+7)4dx=512u4du

Now apply, the power formula of integrals:

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

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