Compute in two ways the flux integral ‹ S F~ · N dS ~ for F= <2y, y, z2> and S the closed surface formed by the paraboloid z = x2 + y2 and the disk x2 + y2 ≤ 4 at z = 4. Use divergence theorem to solve one way, and use SSs F * N ds to solve the other way. (This is a Calculus 3 problem.)
Compute in two ways the flux integral ‹ S F~ · N dS ~ for F= <2y, y, z2> and S the closed surface formed by the paraboloid z = x2 + y2 and the disk x2 + y2 ≤ 4 at z = 4. Use divergence theorem...
Use the Divergence Theorem to calculate the surface integral F · dS; that is, calculate the flux of F across S. F(x, y, z) = (6x3 + y3)i + (y3 + z3)j + 15y2zk, S is the surface of the solid bounded by the paraboloid z = 1 − x2 − y2 and the xy-plane. S
2. Follow the steps to verify the Divergence Theorem forF(x, y, z)-(z2, 2y, 49) and the solid cylinder E : r2 + y2 < 4, 0 2. (a) 9 pts] Evaluate F dS directly where S is the closed cylinder S which bounds E oriented outward. Note that S consists of three surfaces: S1 the surface of the cylinder x2 + y-4 for 0 z 2, the disc Di : x2 +92-4 which lies in the plane z 0 and...
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...
(2) Let F zi + xj+yk and consider the integral vx Fi n dS where S is the surface of the paraboloid z = 1-x2-y2 corresponding to 0, and n is a unit normal vector to S in the positive z-direction. (a) Apply Stokes' theorem to evaluate the integral. b) Evaluate the integral directly over the surface S. (c) Evaluate the integral directly over the new surface S which is given by the disk (2) Let F zi + xj+yk...
#4 please 3. (12 pts). (a) (8 pts) Directly compute the flux Ф of the vector field F-(x + y)1+ yj + zk over the closed surface S given by z 36-x2-y2 and z - 0. Keep in mind that N is the outward normal to the surface. Do not use the Divergence Theorem. Hint: Don't forget the bottom! (b) (4 pts) Sketch the surface. ts). Use the Divergence Theorem to compute the flux Ф of Problem 3. Hint: The...
. Use the divergence theorem to findZ Z S F · dS where F = hxz2 , exz, y2 zi and S is the surface of the solid bounded by the paraboloid x = 25 − 2y 2 − 2z 2 and the plane x = 7.
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...
Tutorial Exercise Use the Divergence Theorem to calculate the surface integral ss F. ds; that is, calculate the flux of F across F(x,y,z) 3xy2 i xe7j + z3 k S is the surface of the solid bounded by the cylinder y2 + z2-4 and the planes x4 and x -4. Part 1 of 3 If the surface S has positive orientation and bounds the simple solid E, then the Divergence Theorem tells us that div F dV. For F(x, y,...
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...
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, =...