Calculate ]]], z(x² + y²) dx dy dz, Where V is the volume outside the upper leaf of the cone z² = x² + y² and inside the cylinder x²+²=1, with z≥ 0.

Q: Find the average squared distance between the origin and thepoints on the paraboloid z = 4 - x2 -…

A: Given: Paraboloid: z=4-x2-y2, z≥0 To find the Average squared distance.

Q: nd the volume of the solid generated by revolving the area bounded by y = x2 a axis from [0, 2]…

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Q: Find the area of part of sphere x² + y? + z² = 100 that lies inside x2 + y? = 10x %3D %3D

A: This is a problem of surface integral.

Q: Find the surface area generated when f(x) = sqrt(x) for 0 <= x <=1 is revolved about y = 0.

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Q: Find the volume of a right circular cone with base radius r unites and height h units using the…

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Q: D. Calculate volume enclosed by (z = 8-x² - y²) and (z = x² + y²), (Use order dy dz dx). وكنت طول

A: Given

Q: What is the area of the enclosed surface bounded by the x-axis, x = 2 and y=x2 ?

A: The area under the curve can be calculated by the integration. The formula for the integration is…

Q: Q3) Find volume of body from below z = x² + y² and above z = 1.

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Q: What is the volume of the solid rotated about the x-axis under the curve y = 2x -1 from x = 1 to x =…

A: Volume by disk method: The volume of a shaded region bounded by two curves over the interval [a,b]…

Q: Find the surface area of the portion of the cylinder x² + z² =4 above the rectangle R = {(x,y) |…

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Q: f (x, уy) %3D — 3х — 2у + 6 | R = {(x,y) : 0 <x< 2,0< y< 2 – x )}

A: Given query is to find the area bounded by the region.

Q: The volume of the surface generated by rotating the function f(x) (* > 1) around the x-axis is А. 2т…

A: The cylindrical shell method is used for calculating volume of revolution.

Q: Find a center of mass of a thin plate of density 8 = 5 bounded by the lines y = x and x = 0 and the…

A: Center of mass of the plate is given by  x,y=MyM,MxM here M=∫∫D δx,ydAMx=∫∫D yδx,ydAMy=∫∫D xδx,ydA…