1. The problem statement, all variables and given/known data

Evaluate:

the limit as n goes to [tex]\infty[/tex] of

[tex]\int^{1}_{0} (n^{3/2}x^{5/4})/(1+n^{2}x^{2})dx[/tex]

dx is the lebesgue measure

2. Relevant equations

I thought I could use the monotone convergence theorem or the dominated convergence theorem neither work.

3. The attempt at a solution

the intregrand is dominated by [tex]1/\sqrt{x}[/tex] but [tex]1/\sqrt{x}[/tex] isn't lebesgue integrable.