   Chapter 12.2, Problem 11E ### 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. ∫ 4 x 3 (7 x 4 +12) 3   d x

To determine

To calculate: The value of the integral 4x3(7x4+12)3dx.

Explanation

Given Information:

The provided integral is 4x3(7x4+12)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:

4x3(7x4+12)3dx

Rewrite the integral by multiplying and dividing by 7 as:

1728x3(7x4+12)3dx

Let u=7x4+12, then derivative will be,

du=d(7x4+12)=28x3dx

Substitute du for 28x3dx and u for 7x4+12 in provided integration.

1728x3(7x4+12)3dx=17u3du

Now apply, the power formula of integrals:

undu=

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