Plane Areas

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
Arcs of quarter circles are drawn inside the square. The center of each circle is at each corner of the square. If the radius of each arc is equal to 20 cm and the sides of the square are also 20 cm. Find the area common to the four circular quadrants. See figure below.
 

Problem
The figure shown below is composed of arc of circles with centers at each corner of the square 20 cm by 20 cm. Find the area inside the square but outside the region commonly bounded by the quarter circles. The required area is shaded as shown in the figure below.
 

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