Verify Stokes theorem is true for the vector field F=yi+zj+xk and the surface S the hemisphere x^2+y^2+z^2=1 and y > 0 in positive y axis
(1 point) Verify that Stokes' Theorem is true for the vector field F = y1+ zj + zk and the surface S the hemisphere x2 + y2 +22 = 1, y > 0 oriented in the direction of the positive y-axis. To verify Stokes' Theorem we will compute the expression on each side. First compute curl F ds curl F -j-k The surface S can be parametrized by 5G, t)=(cos(t) sin(s), sin(tsin(s) cos(s) curl F·dS dt ds where 82 curl F dS Now compute F dr The boundary curve C of the surface S can be parametrized by: r(t)-(cos(t), 0 Use the most natural parametrization) 2m dt similar example (online). However If you don't get this in 3 tries, you can see a 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!
