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Triple Integral on Specific Solid

Compute a triple integral over a specific solid that would be very difficult in rectangular coordinates, but easy in parabolic cylindrical coordinates, u, v, z, where
x=(1/2)(u^2-v^2) y=uv z=z

You must come up with the solid. Remember that the Jacobian determinant (u^2+v^2) must be used when transforming an integral to this coordinate system"

The function of the solid should be given in Cartesian coordinates, and please show the work done to convert to parabolic cylindrical coordinates and to compute the actual integral. It should also include a graph of the solid.

Solution Summary

This shows how to construct a triple integral for a solid for the given conditions.