y=e^(-2x) and x+y= 2
find the volume when rotated over line y=4
how do you do this?
you'll need to use a calculator to find the x-values of intersection of the two graphs.
let the x-values of the intersection points be $\displaystyle x = a$ and $\displaystyle x = b$
use the method of washers ...
$\displaystyle R(x) = 4 - e^{-2x}
$
$\displaystyle r(x) = 4 - (2-x)$
$\displaystyle V = \pi \int_a^b (4 - e^{-2x})^2 - [4 - (2-x)]^2 \, dx$