Find the volume of the region that lies under the graph of the paraboloid z = x 2 + y2 +
Chapter 5, Problem 7(choose chapter or problem)
Find the volume of the region that lies under the graph of the paraboloid z = x 2 + y2 + 2 and over the rectangle R = {(x, y) | 1 x 2, 0 y 2} in two ways: (a) by using Cavalieris principle to write the volume as an iterated integral that results from slicing the region by parallel planes of the form x = constant; (b) by using Cavalieris 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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