Solved: Areas of regions Make a sketch of the region and

Chapter 8, Problem 22E

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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 cardioid \(r=4+4 \sin \theta\)

Questions & Answers

QUESTION:

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

The region inside the cardioid \(r=4+4 \sin \theta\)

ANSWER:

Solution 22E

Step 1:

In this problem we need to find the Area of the region inside the cardioid r = 4+ 4sin(

We know that  Area is ; A =

This means that the formula for Area is ;

        A = dA =  ( ).

The given cardioid is ;  r = 4+ 4sin(.

Graph of the region is shown below ;

 

               

Thus, the Area is ;

         

      A = (

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