# Double integral:volume

• March 22nd 2008, 11:46 AM
prescott2006
Double integral:volume
My question is in the attachment.Sorry for any inconvenience.
• March 22nd 2008, 03:23 PM
mr fantastic
Quote:

Originally Posted by prescott2006
My question is in the attachment.Sorry for any inconvenience.

There's no symmetry when calculating this volume.

The graph of $1 - \cos^3 \theta$ is not symmetric over $0 \leq \theta \leq \pi$ ......

$\int_{0}^{\pi/2} 1 - \cos^3 \theta \, d \theta = \frac{\pi}{2} - \frac{2}{3} \neq \int_{\pi/2}^{\pi} 1 - \cos^3 \theta \, d \theta = \frac{\pi}{2} + \frac{2}{3}$ .....