Chapter 10.5, Problem 3E

### 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 = 4 sin θ

To determine

To calculate: The integral that represents the area of shaded region of the figure:

Explanation

Given:

The polar equation is r=4sinÎ¸ and graph is shown as below:

Formula used:

The area of polar co-ordinates is A=12âˆ«Î±Î²r2dÎ¸.

Calculation:

From the above graph it is clear that shaded region lies in first quadrant over which angle Î¸ lies in the range from 0 to Ï€2.

The provided polar equation is r=4sinÎ¸

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