The function F(x,y) = 4x^2y^3 over the disk x^2 + y^2 =1 is supposed to be zero over the disk. I'm wondering how you can see it? I cannot see this or imagine it in 3D. Is it because the function is odd in terms of y? F(x,-y) = -F(x,y) ? independent of wheher x is positive or negative? Because functions like G(x,y) = y^3 is obviously odd and so the double integral would be zero over the same disk, but I have an extra x^2 term. How is one supposed to think this?