Solving Double Integrals: Finding J in R2

[squenshl]

How do I find
J := $$\int\int_U y cos(x + y) dA$$
where U = {(x,y) $$\in$$ R² : 0 $$\leq$$ x $$\leq$$ 2, 1-x $$\leq$$ x $$\leq$$ -2 + 2x}.

I drew the picture & i get 2 triangles but not sure what to do with them. Help please.

 

[rock.freak667]

in rectangular coordinates, dA=dx dy, so the region U describes will give you the limits for the integral.

 

[wakko101]

I think you should only be getting one triangle. Try checking your picture against one generated by a graphing tool.

Cheers,
W. =)

 

[squenshl]

Very true. I got a triangle & J = -0.5717341110 using maple.