Consider the vector field F(x, y, z) = (2x²y, xz², 4yz). Compute the surface integral JS, F F.dS = ·SS,F •nds where S is the surface of the rectangular box bounded by the planes x = 0, x = 1, 2, z = 0, z = 3, and where the normal vector n points towards the = y = 0, y exterior of the box.

Q: a) Compute the surface area of the portion of the plane x+y=z = 0 contained inside the cylinder x² +…

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Q: .3 Evaluate || F · dS, where F = and S is the helicoid with vector equation r(u, v) = 0<u < 1, 0 <…

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Q: 4. Show that the line integral of F = [0, z] around a closed curve in the r- y plane, oriented as in…

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Q: Fs = , S consists of the paraboloid y = x2 + z2 , 0 < y < 1, and the disk x2 + z2 < 1, y = 1.…

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Q: 26. Verify Stokes' Theorem for the vector field F = 2xyi + xj + (y+z)k and surface z = 4x² - y², z ≥…

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