MATH 2E Study Guide - Quiz Guide: Sinj, Surface Integral, Spherical Coordinate System
Document Summary
Partial credit will be given: (10 points) evaluate the surface integral. F ds for f(x, y, z) = xzi + xj + yk, and s is the hemisphere x2 + y2 + z2 = 4, y 0, oriented in the direction of the positive y axis. Using spherical coordinates, s is given by x = 2 sin cos , y = 2 sin sin , z = 2 cos , 0 , 0 . F(r( , )) (r r ) = 16 sin3 cos cos2 + 8 sin3 cos sin + 8 sin2 cos sin . Z (cid:0) sin3 cos + 2 sin2 cos (cid:1) d = 8. 0 (cid:19) sin2 sin4 + 2 1. + sin2 cos ( cos ) (cid:21) .
