Find the surface area of the surface given by the portion of the paraboloid z= x² + y´ that lies inside the cylinder ¤² +y = 25. (Hint: convert to polar coordinates after setting up the integral)

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Q: 312. Evaluate surface integral zdA, where S is surface z = Vx2 + y², 0 < z< 2.

A: to evaluate the given surface integral first we parametrize  the surface

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A: I have appended the formula used in the solution part

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Q: Cannot solve

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Q: Given the curve in polar equation r = 8 cos 0, 0<0 Use integration to find the area of surface…

A: Given the curve in polar equationr=8 cos θ, 0≤θ≤π2.By using the integration to find the area of…

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A: Solution is given below:

Q: Evaluate ∫ ∫ √ (x2+ y2) dA where R is the portion of the annulus 1 ≤ x2 + y2 ≤ 16 with y ≤ 0 using…

A: We have to evaluate the double integral.

Q: 3. Evaluate the iterated integral Y arctan 2 dydx by converting to polar coordinates.

A: Polar coordinates for converting the iterated integral are: x = rcos(θ), y = rsin(θ)dydx = rdrdθ

Q: Sketch and describe the surface created by p=2 csc(ø).

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Q: 7. Use a program to plot the surface generated by the following equation: 4x – 16y + z? = 16

A: we need to plot the following surface generated by, 4x2-16y2+z2=16

Q: r = 3+2 cos 0

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