Calculating Limit of an Integral

[BobSun]

Limit of an integral
1. Homework Statement
Evaluate:
the limit as n goes to \infty of
\int^{1}_{0} (n^{3/2}x^{5/4})/(1+n^{2}x^{2})dx
dx is the lebesgue measure

2. Homework 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 1/\sqrt{x} but 1/\sqrt{x} isn't lebesgue integrable.

 

[HallsofIvy]

?? 1/\sqrt{x}= x^{-1/2} surely is Lebesque integrable on [0,1]. In fact, it is Riemann integrable and its integral from 0 to 1 is just \left 2x^{1/2}\right|_{x=0}^1= 2.