Answer
$V= \frac{\pi}{2}(e^{2}-1)=10.0359$
Work Step by Step
The volume of the solid obtained by rotating the region under the curve $y=e^{x}$
From 0 to 1 about the x-axis is equal to
$V=\int_{0}^{1} A(x) dx$
$=\int_{0}^{1} \pi e^{2x} dx$
$=\pi(\frac{e^{2x}}{2})_{0}^{1}$
Hence, $V= \frac{\pi}{2}(e^{2}-1)=10.0359$