Comparing volumes Let R be the region bounded by y = ln x,
Chapter 1, Problem 65RE(choose chapter or problem)
Comparing volumes Let R be the region bounded by y=ln x, the x-axis, and the line x=a, where a>1.
a. Find the volume \(V_{1}(a)\) of the solid generated when R is revolved about the x-axis (as a function of a).
b. Find the volume \(V_{2}(a)\) of the solid generated when R is revolved about the y-axis (as a function of a).
c. Graph \(V_{1}\) and \(V_{2}\). For what values of a>1 is \(V_{1}(a)>V_{2}(a)\) ?
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