Question

find the area of the shaped reigion r=root 0

Answer 1

find the area of the shaped region r=root θ

Answer 2

find area of circle
divide it by 4 to get area of one portion
total area - area of one portion

Answer 3

@sangya21 It doesn't work that way. That's a spiral.

Answer 4

Sorry I thought thats a circle.

Answer 5

The area's given by
\[\int_{\pi/2}^{2\pi}\int_0^{\sqrt\theta} r~dr~d\theta=\frac{1}{2}\int_{\pi/2}^{2\pi}\theta~d\theta\]