2. Let u be the surface z = sin(x) sin(y) with 0 < x < A and 0 Sy sa shown below, oriented with downward facing normal v

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2 Let U Be The Surface Z Sin X Sin Y With 0 X A And 0 Sy Sa Shown Below Oriented With Downward Facing Normal V 1 (278.88 KiB) Viewed 35 times

2. Let u be the surface z = sin(x) sin(y) with 0 < x < A and 0 Sy sa shown below, oriented with downward facing normal vectors. Let F (x,y,z) = (ex + y, ey +z, ez + x). The goal of this problem will be the evaluate SSu curl 7 .d 5 as efficiently as possible. = 1.0 0.5 0.01 0 Х a. Notice that the boundary curve C of U consists of the edges of the square [0, 1] x [0,1] in the xy-plane. Stoke's Theorem tells us that Sly curl F.25 = 57.27. d Should C be oriented clockwise or counterclockwise as viewed from above? b. The line integral Sc7d7 still isn't very easy. However, there is another surface V (much simpler that U) of which C is the boundary curve as well. Using Stoke's Theorem again, we can say that ] Evaluate SSv curl 7. 5. Be sure to clearly state what V is. Jour 7.25 = 1.7.17 = Jl, curt7.a3. curl