   Chapter 13.2, Problem 20E ### 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 definite integrals in Problems 1-32. ∫ 0 4 ( 3 x 2 − 2 ) 4 x   d x

To determine

To calculate: The value of the integral 04(3x22)4xdx.

Explanation

Given Information:

The provided integral is 04(3x22)4xdx.

Formula used:

If f is a continuous function on the closed interval [a,b], then the value of the definite integral of f that exists on the interval is,

abf(x)dx=F(b)F(a)

Where F(x)=f(x) for all x in closed interval [a,b].

The integral formula,

xndx=xn+1n+1

Calculation:

Consider the provided integral 04(3x22)4xdx

Let the expression

(3x22)=u

Differentiate with respect to x.

d(3x22)=du(6x)dx=du

So, (6x)dx=du

Multiply and divide the numerator by 6 and rewrite the provided integral as

04(3x22)4xdx=04(3x22)4×66xdx=1604(3x22)4×6xdx

Now, substitute the values in terms of u and du and simplify the integral by the use of integral formula xndx=xn+1n+1 as,

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