2. (a) Set up an integral in Cartesian coordinates to find the volume of the solid that lies between the xy- plane and the paraboloid z = 25-2-2. (b) Set up an integral in polar coordinates to find the same volume described above. (c) Set up an integral to find the surface area of the part of the paraboloid z = 25-2-y² that lies above the xy-plane. (You choose which coordinate system to use for this.)

Q: 3. Consider the surface integral| (V × F) n dS, where F = (0, 0, ryz) and S is that portion of the…

A: ANSWER :(a) The given surface integral is ∬s∇×F.nds ; Where F=<0,0,xyz> i,e F⇀=xyz k^  Now we…

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Q: 36. Rectangular to cylindrical coordinates The volume of a solid is (2 rV2r-x² cV4-x-y² dz dy dx.…

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Q: Question 2. Let E be the solid region inside the surface x² + y² + z²: = 25 and above the surface z…

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Q: SS curl F · dS =0 S

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Q: Use polar coordinates to find the volume of the given solid. The solid above the xy-plane that lies…

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Q: 5. Consider the tetrahedron in the first octant (where each coordinate is positive) bounded above by…

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