Chapter 10.5, Problem 4E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Area of a Polar Region In Exercises 3-6, write an integral that represents the area of the shaded region of the figure. Do not evaluate the integral. r = cos 2 θ

To determine

To calculate: An integral that represents area of shaded region provided in the graph:

Explanation

Given:

The polar equation is r=cos2Î¸ and graph of area of shaded region as shown below:

Calculation:

Consider the function r=cos2Î¸

From the given graph petal of rose curve that lies between the radial lines.

The angle Î¸=3Ï€4 and Î¸=5Ï€4 as shown in below graph:

Area of shaded region bounded by graph of r=f(Î¸) between the radial lines Î¸=Î± and

Î¸=Î² is

A=12âˆ«Î±Î²[f(Î¸)]2.dÎ¸=12âˆ«3Ï€45Ï€4[cos2Î¸]2

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