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(2) Suppose V F = (ex: -2yre?",0). Compute SS (V F). ds, where is the upper...
pls show the work clearly
9. Find | V x F ñds where F =< 22,4x, 3y >, the surface S is the cap of the sphere S x2 + y2 + z2 = 169 above xy-plane and the boundary curve C is the boundary of S.
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.
using this formula
2. Evaluate the surface integral F. dS, where F(x, y, z) = xi+yj+zk is taken over the paraboloid z=1 – x2 - y2, z > 0. SA errom bove de SS (-P (- Puerto Q + R) dA dy
How to solve it?
Let F =< -2, x, y2 >. Find S Ss curlF.nds, where S is the paraboloid z = x2 + y?, OSz54.
Evaluate SS Pods where È CM,y,z) = 5 zex, sy, 2-yz?> s is the where s suface of the unit cube in IR R? not including the face Z-0.
2. Let I be the surface of the cone z = V x2 + y2 (without the top) between planes z = 0 and z = 2. Let F =< x,y,z2 >. Calculate the upward directed flux SS FdS (a) Using the Divergence Theorem. (10 points) (b) Without using the Divergence Theorem. (20 points)
(1 point) Calculate ſls f(x, y, z)ds For y = 4 – z2, Is $(x, y, z) ds = 0 < x, z <7; f(x, y, z) = z
5. Evaluate where D is the upper solid hemisphere 2y2+ z2 < 4, z 2 0.
Problem 4: Use the surface integral in Stokes' theorem to evaluate F.dr for the hemisphere S : x2 + y2 + z2 = 9; z > 0, its bounding circle C: 2+9 and the field F-yi- xj. You only have to compute the surface integral, not the line integral. (20 points)
Problem 5. Let a < b and c > 0 and let f be integrable on [ca, cb]. Show that f c Ca where g(a) f(ex)