Determine the value of SJs F.dS where S is the unit sphere and F(x, y, z)...
5- Let F(x, y, z)= (-6x,0,-6z). Evaluate F.dS where S is the cylinder x2z2 = 2, 0 < y < 2 oriented by the unit normal pointing out of the cylinder. 5- Let F(x, y, z)= (-6x,0,-6z). Evaluate F.dS where S is the cylinder x2z2 = 2, 0
Use the Divergence Theorem to evaluate ∫∫S F·dS, where F(x,y,z)=z²xi+(y³/3+sin z) j+(x² z+y²) k and S is the top half of the sphere x²+y²+z²=4 . (Hint: Note that S is not a closed surface, First compute integrals over S₁ and S₂, where S₁ is the disk x²+y² ≤ 4, oriented downward, and S₂=S₁ ∪ S.)
Calculate Sla F.dS where F = (4x®z, 4yºz, 324) 14 – x2 - y², z = 1 – 22 – ya and and S is the surface of the solid bounded by the hemispheres z = the plane z = 0.
1. Suppose F = (-y,x,z) and S is the part of the sphere x2 + y2 + z = 25 below the plane z = 4, oriented with the outward-pointing normal (so that the normal at (5,0,0) is 1). Compute the flux integral curl F.ds using Stoke's theorem.
A B C Parametrize, but do not evaluate, //f(x, y, z) ds, where f(x, y, z) 2y22 and S is the part , where J(,y,) 3 3 and 0 Sys4 of the graph of z2 over the rectangle -2 s . Parametrize, but do not evaluate, F.n ds, where F (,-,z) and S is the sphere of radius 2 centered at the origin. Calculate JJs xyz dS where S is the part of the cone parametrized by r(u, u) (ucos...
7. Evaluate the circulation integral [/s<= x F) .nds where F(x, y, z) = (x + 3,4+2,2 + y) and S is part of the upper part of the sphere r2 + y2 + 2+ = 25 with 3 <=55(you may use any theorem you find helpful).
You are given the following multivariate PDF (z, y, z) ES else fxx,z(x, y, z) = ) 0 where S-((x, y, z) | x2 + y2 + z2-1) (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inscribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of s....
Use Stokes' Theorem to evaluate. 8. Use Stokes, Theorem to evaluate J, ▽ x ที่ do, where F(x, y, z)-(z2yz,yz2,23ezy and s is part of the sphere x2 + y2 + z-5 that lies above the plane z-1. Also, s is oriented upward. 8. Use Stokes, Theorem to evaluate J, ▽ x ที่ do, where F(x, y, z)-(z2yz,yz2,23ezy and s is part of the sphere x2 + y2 + z-5 that lies above the plane z-1. Also, s is oriented...
6. Evaluate the surface integral // F.ds where the surface S is the sphere x2 + y2 + z2 = 4 [ Ꭻ Ꭻs . and F = (xz, -2y, 3.c) with outward orientation. 7. Use the Divergence Theorem to recalculate the surface integral in problem 6.
Let F(x, y, z) (xr,y, z). Compute the outward flux of F: 9y2622 on the bounded region inside of S. However, you may wish to consider the region bounded between S and the sphere of radius 100.) 7/Fthrough the ellipsoid 4c2 36. (Hint: Because F is not continuous at zero, you cannot use the divergence theorem Suppose that E is the unit cube in the first octant and F(z,y, z) = (-x,y, z). Let S be the surface obtained by...