Really simple question, but I'm having trouble grasping this

[IntegrateMe]

Why is the area of the cardioid r = 2sinθ-2 in the first quadrant represented with limits from π to 3π/2 and not with limits from 0 to π/2? Isn't the first quadrant 0 to π/2?

 

[awkward]

r is negative (or zero) for all values of theta, so when theta is between pi and 3 pi / 2, (r, theta) is in the first quadrant.

 

[IntegrateMe]

Actually, never mind, I'm still not understanding this :(

 

[awkward]

Try plotting the point for theta = 5 pi / 4. Maybe you will see it then.