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    Multivariable Calculus : Triple Integral - Cylidrical Coordinates

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    Solve by triple integration in cylindrical coordinates. Assume that each solid has unit density unless another density function is specified: Find the volume of the region bounded above by the spherical surface x^2 + y^2 + z^2 = 2 and below by the paraboloid z = x^2 + y^2

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    https://brainmass.com/math/derivatives/multivariable-calculus-triple-integral-cylidrical-coordinates-16125

    Solution Preview

    We define
    x=rcos(theta)
    y=rsin(theta)
    z=r
    then the jacobian would be r. We must find

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    | | | 1 dx dy ...

    Solution Summary

    A triple integral is calculated.

    $2.19

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