Using Integration Tests for profiling memory consumption

I would like to use my integration tests to get an understanding of the
memory consumption of my rails application (i.e. does the memory
stablize after a number of requests). As the application is a "wizard"
of sorts (i.e. screen "B" is dependent on screen "A") I don't think
apache benchmark is going to be be much use. How can I use my
integration tests to profile memory? How would I call it multiple
times? Concurrently?

Cheers,
Nicholas