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    Multivariable Calculus : Double Integral - The Polar Coordinates

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    Solve by double integration in polar coordinates: Find the volume bounded by the paraboloids z = x^2 + y^2 and z = 4 - 3x^2 - 3y^2

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    https://brainmass.com/math/derivatives/multivariable-calculus-double-integral-polar-coordinates-16112

    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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    Solution Summary

    A double integral is calculated.

    $2.49

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