EXAMPLE 3 Use a double integral to find the area enclosed by a loop of the four leaved rose r = 3 cos(20). SOLUTION From the sketch of the curve in the figure, we see that a loop is given by the region D = (r, 0) 1 - 1 / 4 5 0 s x / 4, 0 s rs 3 cos ( 20) ) . So the area is 3 cos(20) r dr de Video Example () 3 cos(20) do TT/ 4 = cos (20) de -71/4 = (1 + cos(40)) de - It/4 TT/ 4 = -TT/4