MATH 32B Lecture 6: [Wk6.Wed] Parameterizing a Surface

O Evaluate J y2 dx + x dy. where C is the line segment from (-5,-3) to (0,2), by first parameterizing C Evaluate Jcy dx + z dy +x dz, where C consists of the line segment from (4,0,0) to (3, 4,5), by first parameterizing C

Find the area of the surfac. The helicoid (or spiral ramp) with vector equation r(u, v) = u cos(v) i + u sin(v) j v k, 0 u 1,0 v 9π

2. Use Green's Theorem to compute xdy-y dx for C 5. Evaluate F over the surfac z = 0, [Draw t given by r() = 5 cos 2t i + 3 sin 2t J for t e [0,T]