Use an Iterated Integral to find the area of the region bounded by the graphs of the equation.
x^2+y^2=4 , x=0 , y=0
If $\displaystyle x^2 + y^2 = 4$
then $\displaystyle y = \pm \sqrt{4 - x^2}$.
Also note, that since you are bounded by $\displaystyle x = 0$ and $\displaystyle y = 0$, you are stuck in the first quadrant, so we only take the positive square root. Also note that in this region, we have $\displaystyle 0 \leq x \leq 4$ and $\displaystyle 0 \leq y \leq 4$.
Therefore we are trying to find
$\displaystyle \int_0^2{\sqrt{4 - x^2}\,dx}$.