Changing the order of integration

Hey I'm having some trouble with multiple integrals if anyone would care to explain (I think I'm just not using the correct region!)

Quote:

Evaluate

$\displaystyle \int_{x=0}^2\int_{y=\frac{x}{2}}^1 2xy^2 dy dx $

first directly then changing the order of integration

I did the first part and got 0.8 as the answer

just for the second I'm having trouble

I think the surface being integrated over the the triangle bounded by the lines y=x/2 x=0 and y=1 but I may be wrong which gives

$\displaystyle \int_{y=0}^1\int_{x=2y}^2 2xy^2 dx dy$

but the value of that doesnt agree, can anyone explain how to do the limits correctly?

cheers

Simon