MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
The region T is bounded by the graph of y=lnx, the x–axis, the vertical line x=1, and the vertical line x=e.
(a) Describe an integral setup, with respect to y, that would give the volume of the solid obtained when T is revolved about the y–axis.
(b) A second student proposes finding the same volume by integrating with respect to x instead. Describe this alternative setup.
(c) Compare the two approaches from parts (a) and (b). Explain which method leads to simpler computation and justify your answer by discussing the invertibility of the relevant function(s).