# Math Help - Integral-volume by Cylindrical shells

1. ## Integral-volume by Cylindrical shells

Hi, I need help with regards to whether or not I've set this up correctly . The question asks," use the method of cylindrical shells to find the volume.... bounded by the given curves

y=e^x, x=0, and y=pi about the X-axis

V=2(pi)rh dy

Interval=1 to pi
height = ln (y) by solving y=e^x for x=ln y
thickness = dy

So V= ∫[1,pi] 2pi(y-1)(ln(y)) dy

Is this correct? I'm not sure on the radius....

$V = 2\pi \int_1^{\pi} y \cdot \ln(y) \, dy \approx 21.561$
$V = \pi \int_0^{\ln(\pi)} \pi^2 - e^{2x} \, dx \approx 21.561$