1. The problem statement, all variables and given/known data Let M be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x^2 + y^2 = 9, 0 ≤ z ≤ 1, and a hemispherical cap defined by x^2 + y^2 + (z−1)^2 = 9, z ≥ 1. For the vector field F = (zx + z^2y + 2 y, z^3yx+ 8 x, z^4x^2), compute doubleintM (∇×F) ·dS in any way you like. doubleintM (∇×F) ·dS = ? 2. Relevant equations I thought the line integral would make the most sense in solving this - I wanted to take the line integral with respect to the bottom circle. parameterized, it is (3costheta, 3sintheta, 1). Line int = F(r) (rprime) 3. The attempt at a solution I have no idea what's going on here - I tried to take the line integral by saying r=(3sint,3cost,0) Since z=0 for circle the only parts that matter in the F is the 2y and the 8x, but I don't think that's right. Integral w/ limits 0 to 2pi (2(3sintheta),8(3costheta),0) dot product (-3sintheta, 3costheta, 0) Can anyone help me with this one?