Question $2$

The area inside the circle with polar equation $r=2sin()$ which lies between the lines $y=x$ and $y=-x$ can be found using the integral:

${\displaystyle \underset{-\frac{}{4}}{\overset{\frac{}{4}}{}}}2si{n}^2()d$

${\displaystyle \underset{-1}{\overset{1}{}}}2sin()d$

${\displaystyle \underset{-1}{\overset{1}{}}}(2si{n}^2()-1)d$

${\displaystyle \underset{\frac{}{4}}{\overset{\frac{3}{4}}{}}}sin()d$

${\displaystyle \underset{\frac{}{4}}{\overset{\frac{3}{4}}{}}}2si{n}^2()d$

Question $3$