Polar Curves

Problem
Find the area individually enclosed by the following Cardioids:
(A)   $r = a(1 - \cos \theta)$
(B)   $r = a(1 + \cos \theta)$
(C)   $r = a(1 - \sin \theta)$
(D)   $r = a(1 + \sin \theta)$
 

Problem
Find the area enclosed by r = 2a cos² θ.
 

The length of arc in polar plane is given by the formula:

The formula above is derived in two ways.
 

Example 6
What is the area within the curve r² = 16 cos θ?
 

Find the area enclosed by four-leaved rose r = a cos 2θ.
 

Example 3
Find the area inside the cardioid r = a(1 + cos θ) but outside the circle r = a.
 

Example 1
Find the area enclosed by r = 2a sin² θ.
 

The fundamental equation for finding the area enclosed by a curve whose equation is in polar coordinates is...