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, wh...
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...
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- f(z, y,z) = z
Calculate JJs f(x, y,z) dS For Part of the surface z-z", where 0
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...
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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...
Evaluate the triple integral ∭E(x+6y)dV∭E(x+6y)dV where EE is bounded by the parabolic cylinder y=6x2y=6x2 and the planes z=8x,y=12x,z=8x,y=12x, and z=0z=0.
Evaluate the integral: (x) dzdrdy, where B is the cylinder over the rectangular region R-(z, y) є R2 :-1 z 1,-2 y of the zy-plane, bounded below by the surface ะ1-sin|cos y and above by the sur- 2) face of elliptical paraboloid 22-2-4-9
Evaluate the integral: (x) dzdrdy, where B is the cylinder over the rectangular region R-(z, y) є R2 :-1 z 1,-2 y of the zy-plane, bounded below by the surface ะ1-sin|cos y and above by the sur-...
11. F (z, y, z)-(2c3 + уз) i + (уз + z3) j + 3уг z k, S is the surface of the solid bounded by the paraboloid z 1-2 -v2 and the zy-plane Answer 11. F (z, y, z)-(2c3 + уз) i + (уз + z3) j + 3уг z k, S is the surface of the solid bounded by the paraboloid z 1-2 -v2 and the zy-plane Answer
11. F (z, y, z)-(2c3 + уз) i + (уз...
Find y dV, where E is the solid bounded by the parabolic cylinder z = xand the planes y = 0 and 2 = 15 – 3y E
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4) (5pts) the region under the surface z x2+ y4, and bounded by the planes x-0 and y-9 4 2 and the cylinder y x
4) (5pts) the region under the surface z x2+ y4, and bounded by the planes x-0 and y-9 4 2 and the cylinder y x
Use Stokes' Theorem to evaluate S (double integral) curl F · dS. F(x, y, z) = x^2*y^3*z i + sin(xyz) j + xyz k, S is the part of the cone y^2 = x^2 + z^2 that lies between the planes y = 0 and y = 3, oriented in the direction of the positive y-axis.