# area between this curve

• April 13th 2010, 02:25 PM
akilele
area between this curve
y=e^(-2x) and x+y= 2

find the volume when rotated over line y=4

how do you do this?
• April 13th 2010, 02:36 PM
skeeter
Quote:

Originally Posted by akilele
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 $x = a$ and $x = b$

use the method of washers ...

$R(x) = 4 - e^{-2x}
$

$r(x) = 4 - (2-x)$

$V = \pi \int_a^b (4 - e^{-2x})^2 - [4 - (2-x)]^2 \, dx$