   Chapter 5, Problem 80RE ### 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 77–80, evaluate the definite integral using the properties of even and odd functions. ∫ − 1 1 ( x 3 − x )   d x

To determine

To calculate: The definite integral 11(x3x)dx using the properties even and odd function.

Explanation

Given Information:

The provided definite integral is 11(x3x)dx.

Formula used:

The property of even function f(x),

f(x)=f(x)

The property of odd function f(x),

f(x)=f(x)

The integration of even function,

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

The integration of odd function,

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

The general power rule of integrals:

undu=un+1n+1+C

The fundamental theorem of calculus:

abf(x)dx=F(b)F(a)

Here, F is function such that F(x)=f(x) for all x in [a,b]

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