I saw a problem in Advanced Calculus course, it is required to evaluate the following integral:
$\iint x^2/y^2 dxdy$. The region is set bounded by the curves $x=2$, $y-x=0$ and $xy=1$.
My try: I got the boundaries of integration by the curves by which region is defined, then I got the following:
∬_(1/2 1)^22▒〖x^2/y^2 dxdy=7/2〗
Draw a picture. The answer is $\displaystyle \int_1^{2} \int_{1/x} ^{x} \frac {x^{2}} {y^{2}} dydx=\frac 9 4$.
[Note that $xy=1$ and $y-x=0$ meet at $(1,1)$].