Volume of figure revolving around line

[syeh]

Homework Statement

A represents the 1st quadrant area bounded by f(x)=e^(-tanx), y=.01, y=.09, and the y-axis. Write an integral expression for the volume of the figure that results from revolving A around the line x=30.

Homework Equations

The Attempt at a Solution

So, I know that I have to integrate sideways. To do that, I tried putting the equation y=e^(-tanx) into x= form:

y=e^(-tanx)
-tanx=lny
tanx=-lny
x=invtan(-lny)

So now, I'm not sure what to to. I think you have to integrate sideways somehow and then revolve it around the vertical line x=30...?

 

[Mark44]

Question:
A represents the 1st quadrant area bounded by f(x)=e^(-tanx), y=.01, y=.09, and the y-axis. Write an integral expression for the volume of the figure that results from revolving A around the line x=30.

Attempt:
So, I know that I have to integrate sideways. To do that, I tried putting the equation y=e^(-tanx) into x= form:

y=e^(-tanx)
-tanx=lny
tanx=-lny
x=invtan(-lny)

So now, I'm not sure what to to. I think you have to integrate sideways somehow and then revolve it around the vertical line x=30...?

You don't have to "integrate sideways." Have you drawn a sketch of the region A, and of the solid that is formed? You can integrate using washers (horizontal disks of thickness Δy) or shells (with each of thickness Δx. If you use shells, you'll need two integrals, because the upper boundary changes from a horizontal line to the curve f(x) = e^-tan(x).