Question 1:

Let F =. Use Stokes' Theorem to evaluate curlF . dS, where S S consists of the top and the four sides (but not the bottom) of the cube with one corner at (-2,-2,-2) and the diagonal corner at (3,3,3). Hint: Use the fact that if S1 and S2 share the same boundary curve C that curlF . ds = F . dr = curlF . ds JS1 JS2Let F = Use Stokes' Theorem to evaluate F . dr, where C C is the triangle with vertices (8,0,0), (0,8,0), and (0,0,8), oriented counterclockwise as viewed from above