Question

find the area of the region that is bounded by the curve r=sqrt(2sin(theta)) and lies in the sector 0 12 years ago

Answer 1

\[Area:=\int_{\alpha}^{\beta}\frac12[r(\theta)]^2~d\theta\]

Answer 2

for example; a circle of radius 1 from 0 to 2pi ...
\[Area:=\int_{0}^{2\pi}\frac12[1]^2~d\theta\]
\[\left.Area:=\frac12\theta\right|_{0}^{2\pi}=\frac 22\pi-\frac 02\pi=\pi\]