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## Homework Statement

I have the bounds, 0≤y[itex]_{1}[/itex]≤2, 0≤y[itex]_{2}[/itex]≤1, and 2y[itex]_{2}[/itex]≤y[itex]_{1}[/itex].

I now have a line u=y[itex]_{1}[/itex]-y[itex]_{2}[/itex] and I'm trying to find the area such that y[itex]_{2}[/itex]≥y[itex]_{1}[/itex]-u.

The integral comes down to two parts, the first of which I'm stuck on (when 0≤y1≤1). I'm pretty sure I have one way setup correctly, when I take the integral of dy2 first and then dy1, but for some reason I cannot get the double integral of dy1dy2 to workout properly. This is what I have the setups as:

[itex]\int^{u}_{0}[/itex][itex]\int^{u+y_{2}}_{2y_{2}}dy_{1}dy_{2}[/itex] = u[itex]^{2}[/itex]/2 (This is the one I believe is correct)

[itex]\int^{2u}_{0}[/itex][itex]\int^{y_{1}/2}_{y_{1}-u}dy_{2}dy_{1}[/itex] = u[itex]^{2}[/itex] (This is the one I cannot get to match the first)

Any insight would be very much appreciated. I'm not sure what bounds I'm messing up, but I'm sure that's it.

Thanks!

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