   Chapter 5.4, Problem 65E ### 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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# Using Properties of Definite Integrals Use the value ∫ 0 1 x 2 d x  = 1 3 to evaluate each definite integral. Explain your reasoning.(a) ∫ − 1 0 x 2 d x   (b) ∫ − 1 1 x 2 d x    (c) ∫ 0 1 − x 2 d x

(a)

To determine

To calculate: The definite integral of function 10x2dx using the 01x2dx=13.

Explanation

Given Information:

The definite integral function is 10x2dx.

Formula used:

Integration of even and odd functions

1. If f is an even function, then,

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

2. If f is an odd function, then

aaf(x)dx=0

Calculation:

Consider the definite integral function is, 01x2dx=13

The function is y=x2 and this can be graphed by the below table,

 x −2 −1 1 2 y 4 1 1 4

Therefore, the graph is,

(b)

To determine

To calculate: The definite integral of function 11x2dx using the 01x2dx=13.

(c)

To determine

To calculate: The definite integral of function 01x2dx using the 01x2dx=13.

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