   Chapter 13.2, Problem 15E ### 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. ∫ 2 4 ( x 2 + 2 ) 3 x   d x

To determine

To calculate: The value of the integral 24(x2+2)3xdx.

Explanation

Given Information:

The provided integral is 24(x2+2)3xdx.

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 for any variable u,

undu=un+1n+1

Differentiation formula is,

Differentiation of un with respect to u is nun1

Calculation:

Consider the provided integral

24(x2+2)3xdx

Let the expression

(x2+2)=u

Differentiate with respect to x.

d(x2+2)=du2xdx=du

So, 2xdx=du

Multiply and divide the numerator by 2 and rewrite the provided integral as

24(x2+2)3xdx=24(x2+2)322xdx=1224(x2+2)32xdx

Now, substitute the value of u and du</

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