What is the volume of the solid produced by revolving f(x)=e^xsinpix, x in [0,2] around the x-axis?

1 Answer
Mar 18, 2016

$\pi \cdot {\int}_{0}^{2} {e}^{2 x} \cdot {\sin}^{2} \left(\pi \cdot x\right) \mathrm{dx} = \frac{{e}^{4} \cdot {\pi}^{3} - {\pi}^{3}}{4 {\pi}^{2} + 4}$

Explanation:

And yes, that was friggin wacked.

Here's a Maple rendering of the solid....also, equally wacked.

Here's the 2D rendering in the Cartesian plane!