I need to compute the integral $\int \int_{R} y e^{xy}dA$ for $[0,3]\times [0,1]$.
In the solutions, it has the double integral rewritten as $\int\int_{R} y e^{xy} dA = \int_{0}^{3} \int_{0}^{1} x e^{xy} dydx$.
I'm assuming that some change of variables has taken place here in order for the integrand to go from $y e^{xy}$ to $x e^{xy}$ but I don't understand exactly how. Could somebody please explain this to me in as detailed a fashion (pictures would be good, but not essential) as possible?
Thank you for your time and patience
It is a typo, because $$\int\int_{R} y e^{xy} dA = \int_{0}^{3} \int_{0}^{1} x e^{xy} dy dx$$ is not correct. The correct form is $$\int\int_{R} y e^{xy} dA = \int_{0}^{3} \int_{0}^{1} y e^{xy} dy dx=\int_{0}^{1} \int_{0}^{3} y e^{xy} dx dy $$