I'm refreshing myself with multivariate calculus and I came across this problem:
Calculate the area of the region bounded by $\sqrt x + \sqrt y = \sqrt a$ and $\ x + \ y = \ a$.
I was just wondering how to find the limits of integration given this information.
Set the equations up to each other to find their points of contact.
$\sqrt x + \sqrt y = \sqrt a$
Squaring both sides...
$x+2\sqrt{xy}+y=a$
$x+2\sqrt{xy}+y=x^2+y^2$
Set the integrals up from the two equations' $x$ (coordinate)point(s) of contact.