# How do you find the volume bounded by y=e^x and the lines y=0, x=1, x=2 revolved about the y-axis?

Volume$= \frac{\pi}{2} \left({e}^{4} - {e}^{1}\right)$
According to second theorem of Guldino, volume obtined by a rotation of a section bounded by a function $f \left(x\right)$ and the $x$axis between $a$ and $b$ is $V = \pi {\int}_{a}^{b} {f}^{2} \left(x\right) \mathrm{dx}$.
In our case, we have $V = \pi {\int}_{1}^{2} {e}^{2 x} \mathrm{dx} = \frac{\pi}{2} \left({e}^{4} - {e}^{1}\right)$.