The region under a continuous non-negative function on the interval is revolved about…
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
The region under a continuous non-negative function f on the interval 1≤x≤5 is revolved about the x-axis, producing a solid of volume V. A second solid is formed by revolving the region under y=3f(x) over the same interval about the x-axis, producing volume W.
(a) Express W in terms of V without performing explicit integration.
(b) Explain, in one or two complete sentences, why your result in part (a) must hold for any continuous non-negative function on that interval.