Use the Divergence Theorem to evaluate S Ss F.dS where F= = (5x8, 6yz4, -40z?) and...
Use the Divergence Theorem to evaluate S Ss F.ds where F = (9xy?, 9x’y, 12) and S is the boundary of the region defined by x2 + y2 = 16 and 0 Sz55. The surface integral equals
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
6. Evaluate the surface integral // F.ds where the surface S is the sphere x2 + y2 + z2 = 4 [ Ꭻ Ꭻs . and F = (xz, -2y, 3.c) with outward orientation. 7. Use the Divergence Theorem to recalculate the surface integral in problem 6.
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. (1 point) Use the Divergence Theorem to evaluate FdS where F2x +3 tan2).^z-1 and S is the top half of the sphere x2 +y2 + z2 -9 Hint: S is not a closed surface. First compute integrals overs, and S2 , where S, is the disk x2 + y2 < 9, z = 0 oriented downward and S2 = S U...
Sle Evaluate the surface integral F.ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x2 i + y2 j + z2 k S is the boundary of the solid half-cylinder OSZS25 - y2,0 5x54 250 x
Evaluate the surface integral F.ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation F(x, y, z) = yi - xj + Szk, S is the hemisphere x2 + y2 + z2 = 4, z 20, oriented downward -8751 x
15. Use the Divergence Theorem to evaluate the surface integral F dS triple iterated integral where as a F= (-2rz 2yz, -ry,-xy 2rz - yz) and E is boundary of the rectangular box given by -1< x< 3, -1<y< 3 and z2 1 15. Use the Divergence Theorem to evaluate the surface integral F dS triple iterated integral where as a F= (-2rz 2yz, -ry,-xy 2rz - yz) and E is boundary of the rectangular box given by -1
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.
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, =...
Il Evaluate the surface integral F.ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = y) - zk, S consists of the paraboloid y = x2 + 22,0 Sys1, and the disk x2 + z2 s 1, y = 1. Evaluate the surface integral F.ds for the given vector field F and the oriented surface S....