Areas of regions Make a sketch of the region

Chapter 8, Problem 23E

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QUESTION:

Make a sketch of the region and its bounding curves. Find the area of the region.

The region inside the limacon \(r=2+\cos \theta\)

Questions & Answers

QUESTION:

Make a sketch of the region and its bounding curves. Find the area of the region.

The region inside the limacon \(r=2+\cos \theta\)

ANSWER:

Solution 23E

Step 1:

         In this problem we need to find the Area of the region inside the limacon r = 2 + cos(

The limacon is a  polar curve of the form r = b+acos(

We know that  Area is ; A =

This means that the formula for Area is ;

                   A = dA =  ( ).

The given cardioid is ;  r = 2 + cos(.

Graph of the region is shown below ;

                             

Thus, the Area is ;

         

 A = ( 

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