1. ## Perpendicular Cross Section

i completely forgot how to do these type of problems:

the base of a solid is the region bounded by y=e^(-x), the x-axis, the y-axis, and the line x=1. each cross section perpendicular to the x-axis is a square. find the volume of the solid and keep your answer in terms of e

2. the cross-sectional area is $A(x) = (e^{-x})^2$

$V = \int_0^1 (e^{-x})^2 \, dx$

$V = \left[-\frac{1}{2}e^{-2x}\right]_0^1 = \frac{1}{2}\left[1 - \frac{1}{e^2}\right]$