Chapter 14.3, Problem 44E

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11th Edition

Ron Larson + 1 other

ISBN: 9781337275347

Textbook Problem

AreaIn Exercises 41–46, use a double integral to find the area of the shaded region.

To determine

**To calculate:** The area of the shaded region of the figure using the double integration.

Explanation

**Given:**

The figure is

The expression of *r* is

**Formula used:**

The integration of:

**Calculation:**

From the figure, it can be observe that the radius of the curve varies from zero to

For the variation of the angle

For

The curve has a period of

From obtained data, setup the double integral in polar coordinates for the area of the shaded region:

The expression for the double integral is,

Sect-14.1 P-1ESect-14.1 P-2ESect-14.1 P-3ESect-14.1 P-4ESect-14.1 P-5ESect-14.1 P-6ESect-14.1 P-7ESect-14.1 P-8ESect-14.1 P-9ESect-14.1 P-10E

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