   Chapter 12, Problem 7T ### 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. 7 .  ∫ ( 3 x 2 − 6 x + 1 ) − 3 ( 2 x − 2 ) d x

To determine

To calculate: The evaluation of the integral (3x26x+1)3(2x2)dx.

Explanation

Given Information:

The provided integral is,

(3x26x+1)3(2x2)dx

Formula used:

According to the power rule of derivatives:

ddx(xn)=nxn1

Power rule for Integration:

For any integer n, n1,

xndx=xn+1n+1+C

Calculation:

Consider the provided integral,

(3x26x+1)3(2x2)dx

Simplify as:

(3x26x+1)3(2x2)dx=13(3x26x+1)3(6x6)dx

Let u=(3x26x+1)

Differentiate above equation with respect to x as:

dudx=6x6du(6x6)=dx

Substitute du(6x6) for dx and u for (3x26x+1) in the above integral to get:

(3x26x+1)3(2x2)dx=13(3x26x+1)3(6x

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