Question

Ok so this is a Disc Method Calculus problem:

I have a graph of y=e^x, y=1-x and x=1

I need to find the volume of the solid obtained by revolving the region around the vertical line x=1

Answer 1

When using the disc method
\[\int\limits\limits \pi( R^2-r^2)dx\]
where the radii are perpendicular to the axis where you are rotating, as I like to think.

Answer 2

please you have to subdivide the integration region in two subset, so you have to apply the subsequent formula:
\[V = \int\limits_0^1 {\pi dz} \left[ {1 - {{\left( {1 - z} \right)}^2}} \right] + \int\limits_1^e {\pi dz} \left[ {1 - \ln z} \right]\]
where V is the requested volume