You were right on both accounts. I had meant to integrate from 0 to infinity (whoops!) & T instead of t in the solution.

A few follow up questions then:

1) Why did you decide to choose  m/(Pi*k*T) > 0 ?

2)  Is there any way to  get Maple to format the output  to an improper fraction:  ((8*k*T)/(Pi*m))^(1/2)? I tried simplify(sol,radical), but  it still doesn't want to combine all the terms. This isn't a big deal, it's just bugging me. Thanks again for the help :)