Polar Area

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 bounded by $r = a \sin 3\theta$ and $r = a \cos 3\theta$.
 

Problem
Find the area bounded by $r = a \sin 2\theta$ and $r = a \cos 2\theta$.
 

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

Problem
Find the area enclosed by the following:

Problem
A goat is tied outside a silo of radius 10 m by a rope just long enough for the goat to reach the opposite side of the silo. Find the area available for grazing by the goat. Note that the goat may not enter the silo.
 

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.