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

Example 6
Find each of the two areas bounded by the curves y = x³ - 4x and y = x² + 2x.
 

Example 5
Find the area between the curves 2x² + 4x + y = 0 and y = 2x.
 

Example 4
Solve the area bounded by the curve y = 4x - x² and the lines x = -2 and y = 4.
 

Example 2
Find the volume generated when the area in Example 1 will revolve about the y-axis.
 

Example 1
Find the volume of the solid generated when the area bounded by the curve y² = x, the x-axis and the line x = 2 is revolved about the x-axis.
 

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

Example 3
Find the area bounded by the curve x = y² + 2y and the line x = 3.
 

Example 2
Find the area bounded by the curve a² y = x³, the x-axis and the line x = 2a.