Please, help with this integration problem Consider the region bounded by the curves $y=e^x$, $y=e^{-x}$, and $x=1$. Use the method of cylindrical shells to find the volume of the solid obtained by rotating this region about the y-axis.
I drew the corresponding graph. I'm confused by the fact that the area is rotating about one of the bounding lines (x=1) that bound the region (I have solved volumes this way, until now), but about the y-axis, which is a previous point to the bounding line. How does this changes the procedure?
Thank you!

Interesting Question indeed.
I assume that you know the concepts of cylindrical shells already.
Let R be the region by functions  g(x)  and  f(x)  on an interval x=[a,b] where 
g(x) > f(x) on that interval. Then the volume of revolution obtained by rotating 
the region about the y-axis using cylindrical shell is given by the formula

V = 2*pi*integral of x(R) dx = 2*pi*integral of x(g(x)-f(x)) dx

[I really dont know how to use the math symbols on here so i will post an image of my work]
Here is an image of the bounded region. 

The limits of integration then are a=0, b=1.

If you want to learn about the concepts go here http://www.mhhe.com/math/calc/smithminton2e/cd/folder_structure/text/chap05/section03.htm.
