1. ## integration question

the integral from 0 to phi of sin^2 theta d(theta)
=[theta/2 -sin(2theta)/4 ] from 0 to phi

Can you explain to me how to arrive the second step ? I don't get it ! Thank you very much.

2. I will use x instead of phi.

$\int{sin^{2}(x)}dx$

Use the identity: $sin^{2}(x)=\frac{1}{2}(1-cos(2x))$

$\frac{1}{2}\int{[1-cos(2x)]}dx=\frac{1}{2}x-\frac{1}{4}sin(2x)+C$

3. galactus gave the simplest way, another one could be

$\int\sin^2x~dx=\color{blue}\int\sin{x}\sin{x}~dx$

and apply integration by parts.