Question

Help would be greatly appreciated!!

1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped like a parallelogram, and its boundary aS (with positive orientation) is made up of four line segments. Compute the line integral fos F -dr where F(z, y, z) = 〈エ2018 + y, 2r, r2-Ins). Hint: use Stokes' theorem to transform this line integral over the closed boundary curve aS into a surface integral over the plane segment S. Then transform that surface integral into a double integral over a rectangle and compute it. 2. Let S be the unit sphere (implicit equation z2y22 1 and let F be the vector field 3 Compute the surface integral F dS Hint: apply the divergence theorem. You can use a well-known volume formula instead of actually calculating a triple integral, but make sure you explain your reasoning clearly

Answer 1

2 v Ju dlv φ乍..h |(v xī·ds 스-y