   Chapter 10.5, Problem 3E

Chapter
Section
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=4sinθ and graph is shown as below:

Formula used:

The area of polar co-ordinates is A=12αβr2dθ.

Calculation:

From the above graph it is clear that shaded region lies in first quadrant over which angle θ lies in the range from 0 to π2.

The provided polar equation is r=4sinθ

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