Question

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

Answer 1

`pi*int_0^2 e^(2x)*sin^2(pi*x)dx=(e^4*pi^3-pi^3)/(4pi^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!