   Chapter 13.2, Problem 16E ### 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 1 5 x 2 ( 4 x 3 - 2 ) 4   d x

To determine

To calculate: The value of the integral 015x2(4x32)4dx.

Explanation

Given Information:

The provided integral is 015x2(4x32)4dx.

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 value of the integral xndx=xn+1n+1.

Calculation:

Consider the integral 015x2(4x32)4dx.

Let the expression

(4x32)=u.

Differentiate with respect to x.

d(4x32)=du12x2dx=du

So, 12x2dx=du

Multiply and divide the numerator by 12 and rewrite the provided integral as

015x2(4x32)4dx=015×1212x2(4x32)4dx=51201(4x32)412x2dx

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

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