Use the Divergence Theorem to calculate the surface integral F. aS; that is, calculate the flux of F across S. F(x, y, 2) = 3xy²i + xe²j + z°k, S is the surface of the solid bounded by the cylinder y + z² = 1 and the planes x = -3 and x = 3.

Q: 1) Find the outward flux of F across the region D where F= (6x² + 2xy, 2y + x²z, 4x² y³ ) and the…

A: The vector field is,F¯=6x2+2xy, 2y+x2z, 4x2y3The region D is cut from the first octant by the…

Q: Evaluate | F dr where Cis the intersection of the surfaces y =x' and z =x' from the origin to…

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Q: Compute the surface integral of the function f(x, y, z) = 2xy over the portion of the plane 2x + 3y…

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Q: Let S be the surface given by x² + y²+2z² = 1, x > 0, y ≥ 0, z ≥ 0. Find the flux of (z, 0, 0)…

A: Step 1:The surface S given by x2+y2+2z2=1 is an ellipsoid, and we are considering the upper half…

Q: (x², y², z(x² + y²)) around any closed curve on the surface of Show that the circulation of F = the…

A: Circulation of vector field F around a close curve C = ∫CF.ds If parametric equation of curve C…

Q: (1) Let F(r, y, z) = (y², e², z). (a) Compute the divergence of F. (b) Use the divergence theorem to…

A: Answer

Q: Evaluate f (x-y) dV, where E is the solid E in the first octant bounded by the surface z=1-² and the…

A: In the given problem we have to evaluate the integral                                       where…

Q: Exercise 1. A student is asked to prove If m is even and n is odd, then m² + n² is odd. 2 The…

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Q: Integrate VX F, F = (3y, -xz, -yz) over the portion of the surface 2z = x² + y² below the plane z =…

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Q: Evaluate f. F dS where F(x,y, z) = (4x³z, 4y³z, 3z*) and S is the surface of the solid bounded by…

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Q: 2) Find the area of the surface r(u,v)=u cos vi+u sin vj+2vk where 0su<3 and 0<vs 2n .

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