One way to set up the integral is to write it as
[tex]\displaystyle\iint_Re^{y/x}\,\mathrm dA=\int_{x=0}^{x=1}\int_{y=0}^{y=x^2}e^{y/x}\,\mathrm dy\,\mathrm dx[/tex]
In the opposite order, you could use the equivalent
[tex]\displaystyle\iint_Re^{y/x}\,\mathrm dA=\int_{y=0}^{y=1}\int_{x=\sqrt y}^{x=1}e^{y/x}\,\mathrm dx\,\mathrm dy[/tex]
It's not clear whether you actually have to evaluate the integral or not; I suspect no, since either integrand taken with respect to [tex]x[/tex] does not have an elementary antiderivative.
