009C Sample Final 3, Problem 8

From Math Wiki
Jump to navigation Jump to search

A curve is given in polar coordinates by  

(a) Sketch the curve.

(b) Find the area enclosed by the curve.

The area under a polar curve     is given by

         for appropriate values of  


9CSF3 8.jpg


Step 1:  
The area enclosed by the curve,    is


Step 2:  
Using the double angle formula for    we have


Step 3:  
Lastly, we evaluate to get


Final Answer:  
    (a)     See above

Return to Sample Exam