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1. Homework Statement

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. 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 [tex]1/\sqrt{x}[/tex] but [tex]1/\sqrt{x}[/tex] isn't lebesgue integrable.