# 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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#### 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

$2.49