Calculus III

Prompt

Consider the surface S = {(x, y, z) in R^3 : y = x^2 + z^2, 1 < y < 4}, oriented according to the unit normal vector n = (n_x, n_y, n_z), where n_y < 0. (a) Calculate the area of S. (b) Calculate the flux of G(x, y, z) = (-xy, y^2, -yz) through S in the direction of n, using the Divergence Theorem. (c) Calculate the flux of G(x, y, z) = (-xy, y^2, -yz) through S in the direction of n, using Stokes' Theorem.