Where F(x,y,z)=5e^(xy)I-3e^(xz)j+2x^2zk and S is half of the ellipsis 4x^2+y^2+4z^2=4
(1 point) Use Stokes' Theorem to evaluate curl F dS where F(x, y, z) 5ezy1-3ezij + 2x22k and S is the half of the ellipsoid 4x2 + y2 + 4z2-4 that lies to the right of the zz-plane, oriented in the direction of the positive y-axis Since the half ellipsoid is oriented in the direction of the positive y-axis the boundary curve must be transversed clockwise A parametriza r(t) = cos(t) i+ 0 when viewed from the left. tion for the boundary curve C can be given by: (use the most natural parametrization) curl F.dS dt curl F·dS If you don't get this in 3 tries, you can see a similar example (online). However, try to use this as a last resort or after you have already solved the problem. There are no See Similar Examples on the Exams!
