I've been given the double integral $\displaystyle \int_{x= 0}^{1}\int_{y=x}^{3x}xy dydx $ and instructed to change the order of integration and solve. After solving the given integrals I found they equaled 1.

I reasoned that the initial graph is bounded by two lines y=x and y=3x and bounded on the x-axis between x=0 and x=1; this formed a skewed sort of triangle.

Here's what I changed it to: $\displaystyle \int_{y= 0}^{3}\int_{x=(1/3)y}^{x}xy dxdy $

I either I'm I'm messing up or my professor's solution is wrong...help?