Volumes of Revolution

Need help with this annoying question :|

Q: A drinking glass is modelled by rotating the graph of y = e^x about the y-axis, for 1<y<5. Find the volume of the glass.

- I'm going to make x the subject if we're rotating around the y axis. Thus x = (ln y) ^ 2

Now I don't know how to integrate that.

I tried substituion..

But du/dx = 1/y

Help?

But du/dy = 1/y

I changed the limits into terms of x as opposed to y. And followed it through. I got 12(pi) units ^3.

Has anyone done it ?

I made have made a slip, but I made it:

$5 (\ln 5)^2 -10\ln 5 +8$ times pi!


from

$\displaystyle\pi\int_0^{\ln 5} u^2 e^u\;du$

(e^x) ^ 2 = e ^2x don't it ?

Are you a doctor now?