## Calculus 10th Edition

$\frac{\pi}{2}(1-\frac{1}{e^2})$
Setup the integration using disk method about the x-axis $\pi \int_0^1 (e^{-x})^2dx$ $\pi \int_0^1 (e^{-2x})dx$, integrate $-\frac{\pi}{2}[e^{-2x}]_0^1$, evaluate the definite integral $-\frac{\pi}{2}(e^{-2} -1)$ $\frac{\pi}{2}(1-\frac{1}{e^2})$, simplify