Solution Found!
Areas of regions Make a sketch of the region
Chapter 8, Problem 23E(choose chapter or problem)
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 = (