Let m be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x^2 + y^2 = 81,\ 0 \le z \le 1, and a hemispherical cap defined by x^2 + y^2 + (z-1)^2 = 81,\ z \ge 1. for the vector field \mathbf{f} = (zx + z^2y + 7 y,\ z^3yx + 2 x,\ z^4x^2), compute \iint_m (\nabla \times \mathbf{f}) \cdot d\mathbf{s} in any way you like.