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    Cavalieri's principle

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    Find the volume of the region that lies under the graph of the paraboloid z = x^2 + y^2 + 2 and over the rectangle R = {(x, y) | -1
    and
    in two ways

    (a) by using Cavalieri's principle to write the volume as an iterated integral that results from slicing the region by parallel planes of the form x = constant

    and

    (b) by using Cavalieri's principle to write the volume as an iterated integral that results from slicing the region by parallel planes of the form y = constant.

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    https://brainmass.com/math/integrals/cavalieri-s-principle-double-integrals-24074

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    Solution Summary

    This uses Cavalieri's principle to find volume in two ways: slicing the region into plans of the form x= constant and y= constant

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