   Chapter 10.5, Problem 16E

Chapter
Section
Textbook Problem

# Finding the Area of a Polar Region In Exercises 7-18, Find the area of the region.Interior of   r 2 = 6 sin 2 θ

To determine

To Calculate: The area of interior of polar equation r2=6sin2θ.

Explanation

Given:

The polar equation r2=6sin2θ.

Calculation:

The Shaded section of bounded by the curve r2=6sin2θ is:

Now the complete Curve when θ changes from:

1)0 to π2

2)π to 3π2

In the interval [π,3π2] the value of 6sin2θ is negative, which is not possible.

And in the interval [0,π2] the value of 6sin2θ is positive and forms the two petals.

Substitute the values, r2=6sin2θ for r, 2π for β and 0 for α

Therefore, the total area will be:

A=2

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