   Chapter 4.5, Problem 73E

Chapter
Section
Textbook Problem

Even and Odd Functions In Exercises 73-76, evaluate the integral using the properties of even and odd functions as an aid. ∫ − 2 2   sin x   cos   x   d x

To determine

To calculate: The value of the definite integral 22x2(x2+1)dx by the use of the properties of even and odd functions.

Explanation

Given:

The integral is: 22x2(x2+1)dx.

Formula used:

If f(x) is an even function. Then,

aaf(x)dx=20af(x)dx

And if f(x) is an odd function. Then,

aaf(x)dx=0

The integration of xn is:

xndx=xn+1n+1+C

Calculation:

Let, f(x)=x2(x2+1).

Then,

f(x)=(x)2[(x)2+1]=x2(x2+1)=f(x)

So, f(x)=x2(x2+1) is an even function

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