Hey LLLLLL.

First trying to find the region for each petal (in terms of theta) and integrate each petal separately and add them up.

You need to do this because if for example you integrate over petals that balance each other out (or something similar), then you won't get the right answer. It's like when you integrate sin(x) over 0 to 2*pi, the pi - 2*pi region cancels the 0 to pi region out.