The region is bounded by the curves y=cosx, y=e^-3\2x, x=o and is
revolved about the x-axis. The first point at which the curves
intersect in the first quadrant is revolved about the x-axis.

Here is the graph setup that I derived from the given information:
http://img137.imageshack.us/my.php?image=washergraphjk7.jpg

I can see that this has to be solved using the washer method due to
the hole that would result in the center.....so the equation for the
washer method is:
http://img137.imageshack.us/my.php?image=washereqnap7.jpg

and the values for the definite integral are found by taking the x
values where the two graphs intersect.

I was wondering if I this was the correct setup to solve the equation:
http://img105.imageshack.us/my.php?image=washersetupue9.jpg

I wasn't really sure if I setup this right because it seems like the
definite integral was more complicated than it needed to be and ran
into some trouble while trying to solve it.

your setup looks correct to me.  recheck your integration; the
integral you have is not that hard to do.  break into two terms;
integral of pi*cos^2(x)dx, and integral of pi*e^(-3x)dx.  each
integral is fairly easy to do.

-cab

ohhhhhhhhhhh ok. I don't know why it didn't cross my mind to break up
the integrals. Im the one who made it harder than it needed to be.