please use completely simplified exact values only, thank you.
please use completely simplified exact values only, thank you. 8. Evaluate # F. dS if F(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) -xi yj+3 k S is the boundary of the region enclosed by the cylinder x2 + z2-1 and the planes y 0 and x y 2 Evaluate the surface integral F dS for the given vector field F and the oriented surface...
Evaluate the surface integralF 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. S is the boundary of the region enclosed by the cylinder x2 + z2-1 and the planes y O and x y 3 Evaluate the surface integralF F ds for the given vector field F and the oriented surface S. In other words, find the...
please use completely simplified exact values only, thank you. 7. Evaluate F. dr if fr F(x, y, z) = { 2 tan z + In xyz + 4x°y2z2+ 1 + x2' х -1 tan y + 2x^yz2 + y2 + seco y tanº y, Y Υ х tan-1 + 2x4y2z + - + -2 1 + 22 and C is the curve of intersection of z = 1 – y and x2 + y2 = 1.
(c) Let F be the vector field on R given by F(x, y, z) = (2x +3y, z, 3y + z). (i) Calculate the divergence of F and the curl of F (ii) Let V be the region in IR enclosed by the plane I +2y +z S denote the closed surface that is the boundary of this region V. Sketch a picture of V and S. Then, using the Divergence Theorem, or otherwise, calculate 3 and the XY, YZ...
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, v, z)-xiyj+8 k S is the boundary of the region enclosed by the cylinderx2+2-1 and the planes y-o and xy6 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...
Evaluate the surface integral S 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) = xzey i − xzey j + z k S is the part of the plane x + y + z = 7 in the first octant and has upward orientation.
Evaluate the surface integral S 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) = x i − z j + y k S is the part of the sphere x2 + y2 + z2 = 36 in the first octant, with orientation toward the origin
please just the final answer for both Evaluate the surface Integral || 5. ds for the given vector fleld 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 + y2 = 4, 220, oriented downward 26.677 X Evaluate the surface integral llo F.ds for the given vector field F...
Evaluate the surface integral F dot 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. 24. F(x, y, z) = -xi - yj + z’k, S is the part of the cone z = x2 + y2 between the planes z 1 and 2 3 with downward orientation
Evaluate the surface integral lis(r,y,z) (x, y, z) ds where f(x, y, z) = x + y + z and o is the is the surface of the cube defined by the inequalities 0 < x < 5,0 Sy < 5 and 0 <3 < 5. [Hint: integrate over each face separately.] 1 f(x, y, z) ds =