# Multiple integraion

1. Apr 15, 2006

### Shay10825

Hello everyone! I need some help with the following problems.

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2. Use spherical coordinates to find the center of mass of the sphere of radius 7 and centered at the origin in which the density at any point is proportional to the distance of the point from the z-axis.

My work: http://img54.imageshack.us/img54/820/calc26pj.jpg [Broken]

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3. Use a change of variables to find the volume of the solid region lying above the plane region R bounded below by the parallelogram with vertices (0,0), (-2,3), (2,5) and (4,2) and above the surface z = [(3x + 2y)^2]*[sqrt( 2y – x)]

My work: http://img54.imageshack.us/img54/338/calc37so.jpg [Broken]

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4. Find the area of the surface of the graph of f(x,y) = 121 – x^2 – y^2 over the region R = {(x,y) : x^2 + y^2 <= 121}

My work: http://img54.imageshack.us/img54/295/calc45mq.jpg [Broken]

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Any help would be greatly appreciated.

Thanks

Last edited by a moderator: May 2, 2017