1. The problem statement, all variables and given/known data Integrate f(u,v)= v - sqrt(u) over the triangular region cut from the first quadrant by the line u+v=64 in the uv plane. 2. Relevant equations I am assuming u is the equivalent of the x axis in the xy plane and v the equivalent of y in the xy plane. I am taking the triangle as a Type I region. 3. The attempt at a solution limits of integration: 0≤u≤65, 0≤v≤64-u ∫ ∫ v-sqrt(u) dvdu ∫ (1/2)v2 - sqrt(u)v evaluated from v=0 to v=64-u ∫ 2048 - 64u + (1/2)u2 - 64*u1/2 + u3/2 2048u - 32u2 + (1/6)u3 - (2/3)*64*u3/2+(2/5)*u5/2 evaluated from u=0 to u=64 I get a really narley fraction, namely, 4638576/30, which is of course wrong.