Question

Please solve this as detail as possible

Surface integral and line integral must be used

30% 4, Verify Stokes's Theorem by the set given in the following: F2, 2, yl and S(2+/ 1/2, where 0Sz Sh an d 0 S y Note:

Answer 1

Firstly stocks theorem (definition) let S be oriented surface with limit normal N and assume that s is bounded by piece wise smooth tordon curve C whose orientation is compatible with that of S if F^vector is a field that is continuously differentiable on s then integral _c F. dr = double integral _s (curl f. N) ds now given vector field F^vector = [z^2_1 x^2, y^2] and S: z = squareroot x^2 + y^2 where 0 lessthanorequalto z lessthanorequalto h and y greaterthanorequalto 0 so F^vector = z^2 i^+ x^2 j^+ y^2 k^ here s: z = squareroot x^2 + y^2 is a cone H one limit is in the direction of i^ upward) \r\n integral F^vector . dr = integral (z^2 i^+ x^2 j + y^2 k). (dx I + dy j + dz k) = integral (z^2 dx + n^2 dy + y^2 dz) now integral (z^2 dx + n^2 dy + y^2dz