Example 1: Area of a 'Four-leaf Clover'

Figure 7.9.6

Find the area of one loop of the "four-leaf clover" r = sin2θ. From Figure 7.9.6, we see that one loop is traced out when θ goes from 0 to π/2. Therefore the area is

As one would expect, all four loops have the same area.

On the loop from θ = π/2 to θ = π, the value of r = sin 2θ is negative. However, the area is again