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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Checkpoint 8 Worked-out solution available at LarsonAppliedCalculus.com

Evaluate each definite integral.

a. 1 1 x 4 d x

b. 1 1 x 5 d x

(a)

To determine

To calculate: The definite integral 11x4dx by the use of rules for even and odd functions.

Explanation

Given information:

The definite integral is 11x4dx.

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,

11x4dx

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

Here,

f(x)=11

(b)

To determine

To calculate: The definite integral 11x5dx by the use of rules for even and odd functions.

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