# How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region # y = e^ (-x)#, bounded by: #y = 0#, #x = -1#, #x = 0# rotated about the #x=1#?

##### 1 Answer

This looks like:

graph{(y - e^(-x))(y)(x + 1)(sqrt(0.25 - (x + 0.5)^2))/(sqrt(0.25 - (x + 0.5)^2)) <= 0 [-3.29, 5.48, -0.855, 3.52]}

The Shell Method suggests using the formula

where

Rotating it about

The function itself should be

Therefore, you have:

Let's see what

Let:

Overall we have: