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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5.4, Problem 66E
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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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Using Properties of Definite Integrals Use the value ∫ 0 4 x 3 d x = 64 to evaluate each definite integral. Explain your reasoning.

(a) ∫ − 4 0 x 3 d x   (b) ∫ − 4 4 x 3 d x    (c) ∫ 0 4 2 x 3 d x

(a)

To determine

To calculate: The definite integral of function ∫−40x3dx using the ∫04x3dx=64.

Explanation

Given Information:

The definite integral function is ∫−40x3dx.

Formula used:

Integration of even and odd functions

1. If f is an even function, then,

∫−aaf(x)dx=2∫0af(x)dx

2. If f is an odd function, then

∫−aaf(x)dx=0

Calculation:

Consider the definite integral is,

∫04x3dx=64

The function is y=x3 and this can be graphed by the below table,

x −1 0 1
y −1 0 1

Therefore, the graph is,

(b)

To determine

To calculate: The definite integral of function ∫−44x3dx using the ∫04x3dx=64.

(c)

To determine

To calculate: The definite integral of function ∫042x3dx using the ∫04x3dx=64.

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