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    Multivariable Calculus: Triple Integral - Cylindrical Coordinates

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    Question: 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.

    © BrainMass Inc. brainmass.com February 24, 2021, 2:22 pm ad1c9bdddf
    https://brainmass.com/math/integrals/multivariable-calculus-triple-integral-cylindrical-coordinates-16124

    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 ...

    Solution Summary

    This solution is comprised of a detailed, step-wise response which shows how a triple integral is solved. All calculations are included.

    $2.19

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