1 point) Use Stoke's Theorem to evaluate (▽ × F)·dS where M is the hemisphere x2 + y2 + z2-16, x ...
(1 point) (▽ x F) . ds where M is the hemisphere z2 + y2 + z2-25, z > 0, Use Stoke's Theorem to evaluate with the normal in the direction of the positive x direction, and F--(z3,0, y Begin by writing down the "standard" parametrization of aM as a function of the angle 0 (denoted by "t" in your answer) (use "t" for theta). The value of the integral is
(1 point) (▽ x F) . ds where M...
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.
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.
please help me solve the following question
8. Compute JJ f dS where f(x, y, 2)22+2 and S is the top hemisphere x2 + y2 + Z2, 220. 9. Compute JJ F-n dS where F-: (x, y, z) and s is the cone z2 x2 + y2, 0 S 2 1; with the outward pointing normal.
8. Compute JJ f dS where f(x, y, 2)22+2 and S is the top hemisphere x2 + y2 + Z2, 220. 9. Compute JJ...
Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = zeli + x cos(y)j + xz sin(y)k, S is the hemisphere x2 + y2 + z2 = 4, y 2 0, oriented in the direction of the positive y-axis.
mmer 2019 3. Evaluate: M y2 dV where E the solid hemisphere x2 + y2 +z2 9 and y 2 0 indrnse)
mmer 2019 3. Evaluate: M y2 dV where E the solid hemisphere x2 + y2 +z2 9 and y 2 0 indrnse)
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-< x2 sin(z), y2, xy >, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
Evaluate the following integral, ∫ ∫ S (x2 + y2 + z2) dS, where S is the part of the cylinder x2 + y2 = 25 between the planes z = 0 and z = 9, together with its top and bottom disks
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...