   Chapter 10.5, Problem 7E

Chapter
Section
Textbook Problem

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

To determine

To calculate: The value of area of interior region of polar equation r=6sinθ.

Explanation

Given:

The polar equation is r=6sinθ.

Calculation:

Use the following steps in Ti-83 calculator to plot the graph:

Step1: Press [MODE] Key and select POL mode.

Step2: Press (Y=) Key.

Step3: Press r1=6sinθ

Step4: Now press the [GRAPH] key and the graph of the equation is obtained:

Shaded section bounded by the curve r=6sinθ is given away below:

From the figure, it can be seen that θ varies from 0 to π

Therefore, the area of shaded region bounded by graph of r=f(θ) between the radial lines θ=α and θ=β is:

A

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