Solve the problem.
-Find the volume of the solid generated by revolving the region bounded by the curve $y = \ln x$, the $x$-axis, and the vertical line $x = e ^ { 2 }$ about the $x$-axis.
A) $\pi \left( e ^ { 2 } - 1 \right)$
B) $\pi ( e - 1 )$
C) $2 \pi \left( \mathrm { e } ^ { 2 } - 1 \right)$
D) $\pi \mathrm { e }$

Question

Quizplus · Accepted Answer

The volume of the solid is found using the disk method: $ V = \pi \int_{1}^{e^2} (\ln x)^2 \, dx $. Evaluating this integral gives $ 2\pi(e^2 - 1) $.

Solve the Problem y=ln⁡xy = \ln xy=lnx , The xxx -Axis, and the Vertical Line

Solve the Problem $y = \ln x$ , The $x$ -Axis, and the Vertical Line