Use the Divergence Theorem to evaluate ∬SF⋅dS∬SF⋅dS where
F=〈z2x,y33+3tan(z),x2z−1〉F=〈z2x,y33+3tan(z),x2z−1〉
and SS is the top half of the sphere x2+y2+z2=9x2+y2+z2=9.
Use the Divergence Theorem to evaluate ∬SF⋅dS∬SF⋅dS where F=〈z2x,y33+3tan(z),x2z−1〉F=〈z2x,y33+3tan(z),x2z−1〉 and SS is the top half of...
Help Entering Answers (1 point) Use the Divergence Theorem to evaluate F . dS where F =くz2xHFz, y + 2 tan(2), X22-1 and S is the top half of the sphere x2 +y2 25 Hint: S is not a closed surface. First compute integrals over S and S2, where Si is the disk x2 +y s 25, z 0 oriented downward and s,-sus, F-ds, = 滋 dy dx F.dS2 = S2 where X1 = 리= Z2 = IE F-ds, =...
5. Evaluate JSF dS, where and S is the top half of the sphere x2 + y2 + z2-1. Note that S is not a closed surface. Therefore you must first find a surface Sı such that you can (a) Evaluate the flux of F across S (b) Use the divergence theorem on SUSi 5. Evaluate JSF dS, where and S is the top half of the sphere x2 + y2 + z2-1. Note that S is not a closed...
6. Use the Divergence Theorem to evaluate SSF. ds, where Ể(x, y, z) = (x/x2 + y2 + z2 , yvx2 + y2 + z2 , z7 x2 + y2 + z2 ) and S consists of the hemisphere z V1 – x2 - y2 and the disk x2 + y2 = 1 in the xy-plane.
(1 point) Let F(x, y, z) = 1z2xi +(x3 + tan(z))j + (1x2z – 5y2)k. Use the Divergence Theorem to evaluate SsF. dS where S is the top half of the sphere x2 + y2 + z2 = 1 oriented upwards. / F. ds = S
(1 point) Let F(x, y, z) = 1z- xi + (x2 + tan(z)j + (1x²z + 3y2)k. Use the Divergence Theorem to evaluate /s F. ds where S is the top half of the sphere x2 + y2 + z2 = 1 oriented upwards. SSsF. dS =
Provide correct answer Use the Divergence Theorem to evaluate //F. ds where F = (4x", 4y?, 17) and S is the sphere x² + y2 + z = 25 oriented by the outward normal. The surface integral equals
Use the Divergence Theorem to evaluate S Ss F.dS where F= = (5x8, 6yz4, -40z?) and S is the boundary of the sphere 22 + y2 + z2 = 9 oriented by the outward normal. The surface integral equals
(8 points) Evaluate the surface integral SF. dS where F = (1, 32, 3y) and S is the part of the sphere x2 + y2 + z2 = 4 in the first octant, with orientation toward the origin. SSSF. ds
13. Show step by step how to use the Divergence Theorem to set up the surface integral F. dS := Fonds with outward orientation, where F(x, y, z) = (x, z, y) and S is the surface of the unit sphere x2 + y2 + z2 = 1. Do Not Evaluate.
Let F = < x-eyz, xexx, z?exy >. Use Stokes' Theorem to evaluate slice curlĒ ds, where S is the hemisphere x2 + y2 + z2 = 1, 2 > 0, oriented upwards.