   Chapter 5.3, Problem 44E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Evaluate the integral. ∫ − 2 2 f ( x )   d x where   f ( x ) = { 2 if − 2 ≤ x ≤ 0 4 − x 2 if 0 < x ≤ 2

To determine

To evaluate: The integral function 22f(x)dx.

Explanation

Given information:

The integral function is 22f(x)dx.

Here, f(x) is function of x.

Express the function f(x) as shown below.

f(x)={2 if 2x<04x2 if 0<x2 (1)

Calculation:

Modify Equation (1) as follows:

22f(x)dx=202dx+02(4x2)dx (2)

Integrate Equation (2) with respect to x as shown in below

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