   Chapter 13.2, Problem 19E ### 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 2 15 x 3 ( x 4 − 6 ) 6   d x

To determine

To calculate: The value of the integral 2215x3(x46)6dx.

Explanation

Given Information:

The provided integral is 2215x3(x46)6dx.

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

2215x3(x46)6dx

Let the expression

(x46)=u

Differentiate with respect to x.

d(x46)=du4x3dx=du

So, 4x3dx=du

Multiply and divide the numerator by 4 and rewrite the provided integral as

2215x3(x46)6dx=2215×44x3(x46)6dx=15422(x46)64x3dx

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

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