BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 5.2, Problem 34E
To determine

To Find: The integral of 224x2dx

Expert Solution

Answer to Problem 34E

The integral of 224x2dx=2π

Explanation of Solution

Given information:

The integral is:

  224x2dx

Calculation:

  224x2dx

Interpret this integral as the area under the curve y=4x2 from -2to2

But since

  y2=4x2x2+y2=4

Which show the graph of f(x) is the half circle with radius 2 in figure

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 5.2, Problem 34E

Therefore

  224x2dx=12(π(2)2)224x2dx=2π

Hence,

The integral of 224x2dx=2π

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