Question

The area inside the circle with polar equation r= 2sin theta and above the lines with eqautions y=x and y=-x is given by

Answer 1

just set up the equation
is it \[\int\limits_{-\pi/4}^{\pi/4} 2\sin^2 Theta\]

Answer 2

I believe the formula for areas bounded by polar curves is
\[\frac{1}{2}\int_\alpha^\beta r^2~d\theta\]
So yeah, that looks right to me.