   Chapter 10.5, Problem 2E

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 = cos 2 θ To determine

To calculate: An integral that represents area of shaded region provided in the graph: Explanation

Given:

The polar equation is r=cos2θ and graph of area of shaded region as shown below:

Calculation:

Consider the function r=cos2θ

From the given graph petal of rose curve that lies between the radial lines.

The angle θ=3π4 and θ=5π4 as shown in below graph:

Area of shaded region bounded by graph of r=f(θ) between the radial lines θ=α and

θ=β is

A=12αβ[f(θ)]2.dθ=123π45π4[cos2θ]2

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