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Characterizing Power Functions by Volumes of Revolution

1998
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The College Mathematics Journal
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A power function is a function of the form f (x) = x n . We will consider positive multiples of power functions with positive powers, that is, functions of the form f (x) = kx n (k, n > 0) over the domain {x : x ≥ 0}. For r > 0, let R 1 (r) be the first quadrant region under the curve y = f (x) over an interval [0, r], and let R 2 (r) be the first quadrant region to the left of R 1 (r), as shown in Figure 1 below. Revolve these regions R 1 (r) and R 2 (r) around the y-axis to get solids of

doi:10.2307/2687636
fatcat:zn74pybtyfbf7knhir4xdfkkrm