I want to calculate the following areas of f over S :
a) $S$ is given by the area enclosed by : $y=1, x=3, y=2x$ and $\displaystyle f(x,y) = \frac{x^{2}}{y^{2}}$.
b) $S$ is given by the area enclosed by : $x=y^{2}-4$, $x=3y$ and $f(x,y)= 1$
I calculated the following for a)$\int_{\frac{1}{2}}^{3}\left(\int_{1}^{2x}\frac{x^{2}}{y^{2}} dy\right) dx.$
for b) I switched $x$ with $y$ and calculated this: $\int_{-1}^{4}\left(\int_{-3}^{x^{2}-4} 1dy\right)dx.$
Is this correct? I draw $S$ and look at the intersection points. Still I have problem determining the right boundaries for my integrals. Can you give me a hint/idea what is a good way to find boundaries?
Merci.