# Solids Of Revolution

• Mar 4th 2009, 06:17 AM
qzno
Solids Of Revolution
Find the volume of the solid that is generated by rotating around the indicated axis the plane region bounded by the given curves. Sketch the region and a typical rectangle that generates a 'disc' or 'washer'.

$y=2e^{-x}$ , $x=0$ , $y=1$ , about the x-axis.
• Mar 4th 2009, 08:08 AM
skeeter
Quote:

Originally Posted by qzno
Find the volume of the solid that is generated by rotating around the indicated axis the plane region bounded by the given curves. Sketch the region and a typical rectangle that generates a 'disc' or 'washer'.

$y=2e^{-x}$ , $x=0$ , $y=1$ , about the x-axis.

method of washers ... $V = \pi \int_a^b [R(x)]^2 - [r(x)]^2 \, dx
$

$
R = 2e^{-x}
$

$
r = 1
$

$
a = 0
$

$
b = \ln{2}
$

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