You can't run jsps without installing tomcat but you can use apache as a front for tomcat.
There's at least two ways to do it. The simplest, I think, would be to use apache as a proxy using
mod_proxy. That's very simple because it's a very loose connection between the two. I've never used it so I don't know if it's seamless but it's definitely going to be what I try next time I integrate the two (I'll need to sometime soon).
The more difficult way is mod_jk which is what ugh linked. I haven't tried that way in a while and that documentation looks much more organized than what I used but when I did it, but it was quite difficult. There is also the problem that you always have to start the servers in a certain order for it to work. Not a problem at startup, but if one of them goes down then you might have to restart the other. I don't remember which is which but if tomcat going down required apache to be restarted you might have a real problem. Basically jk is a custom protocol for forwarding http requests (as I understand it, anyway).