Suppose S is the cylinder parametrized as follows: Set up a double integral that represents the surface area of S and evaluate the integral in terms of u and v. r(u, v) = (4 cos u, 4 sin u, v), 0≤ u ≤ 2m, 0 ≤ v ≤ 1.

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Q: Give a contrapositive proof of the following: If n is an odd integer, then the equation x2+ x -n=0…

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Q: Let C be parametrized by x = 3 sin² t and y = 3 sint cost for 0 ≤ t ≤. Find the length L of C. L =

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Q: 2/ MATH

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A: We have to evaluate the triple integral ∭Vzdxdydz where V is the upper half of the ellipsoid

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Q: 21. (y² dx + x² dy)

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Q: Use spherical coordinates to evaluate the triple integral SSSE x2 + y2 + z2 dV, Where E is the ball:…

A: Use spherical coordinates to evaluate the triple integral SSSE x2 + y2 + z2 dV, Where E is the ball:…

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A: Find: ∭Txyz dV Obtain the equation of the plane that contains the points 0, 0, 0, 1, 1, 0 and 1, 0,…

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A: Explanation of the answer is as follows

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A: Stokes theorem is verified

Q: 2. Evaluate the integral by first converting into spherical coordinates: |a²-x²-y² |a²-x²-yz (x²z+…

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Q: By changing to polar coordinates, evaluate the integral where D is the disk x² + y² ≤ 36. Answer =…

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