Solve A = ∫ (from 0 to frac { pi) of {2}}int_2^2(1+cosθ)sin(θ)*kdndθ

$$A = \int _ { 0 } ^ { \frac { \pi } { 2 } } \int _ { 2 } ^ { 2 ( 1 + \cos \theta ) } \sin ( \theta ) \cdot k d n d \theta$$

Solve for A

$$A=k$$

Solve for k

$$\left\{\begin{matrix}k=\frac{2A}{\pi \sin(2\theta )}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\frac{\pi n_{1}}{2}\\k\in \mathrm{R}\text{, }&A=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\frac{\pi n_{1}}{2}\end{matrix}\right.$$