   Chapter 5.4, Problem 64E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Integrating Even and Odd Functions In Exercises 61–64, evaluate the definite integral using the properties of even and odd functions. See Example 8. ∫ − 2 2 ( 1 2 t 6 + 1 )   d t

To determine

To calculate: The definite integral of function 22(12t6+1)dt by the use of rules for even and odd functions.

Explanation

Given information:

The definite integral function 22(12t6+1)dt.

Formula used:

According to the integration of even and odd functions:

1. For even function f,

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

2. For odd function f,

aaf(x)dx=0

Calculation:

Consider the definite integral,

22(12t6+1)dt

As it is known that when f(x)=f(x), then f(x) is an even function,

Here,

f(t)=22(12(t)6+1)dt=

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