Find the flux of F(x, y, z) = (e² + 2x, 3x², y) across the surface S defined by R(u, v) = (u², uv, v), where 0 ≤ u≤ 1,0 ≤v≤ 2. parametrically

Q: Compute the flux of F¹ = 5(x + z)i + 5j + 5zk through the surface S given by y = x² + z², with 0 ≤ y…

A: The given surface is  and .The flux is given by  where  is the vector function that describes the…

Q: 4. Find the flux of F across S if F = yi-xj+2zk and S is the hemisphere x² + y² + z² = 4, z ≥ 0,…

A: We have to find flux passing through sphere.

Q: Compute the flux of F = xi+yj+zk through the curved surface of the cylinder x² + y² = 1 bounded…

A: The given vector field is F→=xi+yj+zk. The goal is to evaluate the flux or surface integral of the…

Q: Draw the parameterized surface

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Q: Find the flux of F(x, y, z) = yi - xj + 2k across S, where S is the helicoid with vector equation…

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Q: 2. Let S be the surface given by r(u, v) = (u, u² + v², v). Find the equation of the tangent plane…

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Q: Find the flux of the vector fleldF = (x – y*)i+ 4yj + x'k out of the rectangular solid [0, 1] x [1,…

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Q: Let F = = (x, y, z) (x² + y² + z²)3/2 Use the fact that V F = 0 when (x, y, z) following surfaces.…

A: Step 1:- To find the flux of the vector field F=(x2+y2+z2)3/2(x,y,z)​ through the given square…

Q: Compute the flux of F = xi+yj+zk through the curved surface of the cylinder x² + y² = 1 bounded…

A: The vector field is F=xi^+yj^+zk^. The curves surface is x2+y2=1 bounded below by the plane x+y+z=2…

Q: Find the flux of F = 3zi + 5y? i+ 3x k out of the closed cone y = Væ2 + z2, with 0 < y < 1. flux =

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Q: Find the flux of G(x, y, z) = (xz)i+ (yz)j+(z²)k outward across the part of the sphere x² + y² +z² =…

A: Here, surface, S={(x,y,z): x2+y2+z2=9, and 1≤z≤2}. For z=1, we get x2+y2=8 and for z=2, we get…