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Calculate JJs f(x, y,z) dS For Part of the surface z-z", where 0 < z, y < 101 ; JJs f(z, y,z) ds-...
e.g.4 Evaluate JJs F dS, where j + sin(zy)k and S is the surface of the region E bounded by the parabolic cylinder z- 1 a2 and the planes z-0,y-0, and y + z-2.
e.g.4 Evaluate JJs F dS, where j + sin(zy)k and S is the surface of the region E bounded by the parabolic cylinder z- 1 a2 and the planes z-0,y-0, and y + z-2.
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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...
11. (20 pts) Consider the surface integral JJs F dS with F(x, y, 2) - 2xyǐ + zeij + z3k where s is the surface of the cylinder y2 + 2 = 4 with 0-x < 2. (a) Parametrize this surface and write down (but do not evaluate) the iterated integrals for the surface integral. (b) Let S' be the closed surface with outward-facing normals obtained by taking the union of the surface S with the planes x = 0...
#P2 The differential of surface area, ds, for a surface determined by the graph of z=f(x,y) is calculated by dS = #P3 The differential of surface area, dS, for a surface determined by the graph of x = f(y,z) is calculated by dS = #P4 True or false: If Fis a velocity vector field for some fluid and S is a semipermeable surface, then the flux integral JJs FindS computes how quickly volume is passing through the surface S.
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 =
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the hemisphere x + y +z2 = 25, for z 2 0 The value of the surface integral is (Type an exact answers, using t as needed.)
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the hemisphere x + y +z2 = 25, for z 2 0 The...
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(1 pt) Calculate S/sf(x, y, z) ds For 231 where 0 Sxys 11- f(x, y, z) = Isf(x, y, z) ds = (192/5)pi Part of the surface x
9. Let Q be the solid bounded by the cylinder x2 + y2 = 1 and the planes z = 0 and z = 1 . Use the Divergence Theorem to calculate | | F . N dS where s is the surface of Q and F(x, y, z) = xi + yj + zk. (a) 67T (d) 0 (b) 1 (e) None of these (c) 3π
9. Let Q be the solid bounded by the cylinder x2 + y2...
f(x, y, z)ds where f(x, y, z) = x=y=z and o is the portion of the plane x+y=1 lying in the first octant o between z = 0 and z= 1. [ f(x, y, z)ds = ? Edit
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be the hemisphere 2 F(x, y,z)-yitj+3z k. Calculate JJs F dS, the flux of F across S
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be...