Under [itex]y = (\sin{x})^{\frac{3}{2}}[/itex] between 0 and pi.

The radius is... [itex]r = (\sin{x})^{\frac{3}{2}}[/itex]

Then the area for any sample is... [itex]A (x) = \pi((\sin{x})^{\frac{3}{2}})^{2}[/itex]

Simplifying to... [itex]A (x) = \pi(\sin{x})^{3}[/itex]

Integrate between 0 and pi to get the volume...

[tex]V = \pi \int_{0}^{\pi} (\sin{x})^{3}[/tex]

[tex]V = \pi [ \frac{(\sin{x})^{4}}{4\cos{x}} ]_{0}^{\pi}[/tex]

But... sin(pi) and sin(0) both equal 0, making the volume 0. But it's actually (4/3)(pi). What am I missing?