   Chapter 12, Problem 6T ### 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 1-11. 6. ∫ 5 x 2 ( 4 x 3 − 7 ) 9 d x

To determine

To calculate: The value of the integral 5x2(4x37)9dx.

Explanation

Given Information:

The provided integral is,

5x2(4x37)9dx

Formula used:

For any non-zero constant c,

cu(x)dx=cu(x)dx

Power rule for Integration:

If u=u(x), then

undu=un+1n+1+C where n1.

Calculation:

Consider the provided integral,

5x2(4x37)9dx

As for any non-zero constant c, cu(x)dx=cu(x)dx. So,

5x2(4x37)9dx=5x2(4x37)9dx

Further, simplify as,

5x2(4x37)9dx=5x2(4x37)9dx=512(4x37)912x2dx

Let u=4x37

Differentiate the above equation with respect to x as:

dudx=12x2du12x2=dx

Substitute du12x2 for dx and u for 4x37 in above integral to get,

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