1. Use Stokes’ Theorem to evaluate ∬ curF⃗ ∙ dS⃗ S where F⃗ = x 3 i⃗ + (4y − z 3y 3 )j⃗ + 2xk⃗⃗ and S is the portion of z = x 2 + y 2 − 3 below z = 1 with orientation in the negative z-axis direction. 2. Use Stokes’ Theorem to evaluate ∬ curF⃗ ∙ dS⃗ S where F⃗ = 2yi⃗ + 3xj⃗ + (z − x)k⃗⃗ and S is the portion of y = 11 − 3x 2 − 3z 2 in front of y = 5 with orientation in the positive y-axis direction. 3. Use Stokes’ Theorem to evaluate ∫ F⃗ ∙ dr⃗ C where F⃗ = (zx 3 − 3z)i⃗ + xzj⃗ + yxk⃗⃗ and C is the triangle with vertices (0,0,4), (0,2,0), and (2,0,0). C has the orientation seen in the sketch below.