   Chapter 10.5, Problem 49E

Chapter
Section
Textbook Problem

# Conjecture Find the area of the region enclosed by r = a cos ( n θ ) for n = 1 , 2 , 3 , … Use the results to make a conjecture about the area enclosed by the function when n is even and when n is odd.

To determine

To Calculate: The area of region enclosed by r=acosnθ for the values of n=1,2,3 and to make the conjecture about the area enclosed by the function when n is even and when n is odd.

Explanation

Given:

Polar equation is r=acosnθ

Formula Used:

Area will be calculated by using integration on r=acosnθ.

Calculation:

Consider the equation r=acosnθ.

For n=1, the equation is r=acosθ

And the area of the circle is πa24

Graph is shown below:

For n=2, equation is r=acos2θ

And the area is:

A=8(12)0π4(acos2θ)2dθ=πa22

Graph is shown below:

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 