y=e^(-2x) and x+y= 2

find the volume when rotated over line y=4

how do you do this?

Printable View

- Apr 13th 2010, 02:25 PMakilelearea between this curve
y=e^(-2x) and x+y= 2

find the volume when rotated over line y=4

how do you do this? - Apr 13th 2010, 02:36 PMskeeter
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}

$

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

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