Infinite Limit of a Complex Integral

[Alphaman]

The problem is as follows:

lim_{n\rightarrow\infty} \int^{1}_{0}√(1+n^{2}x^{2n})

My issue is that I'm unsure as to where to start. We just went over DE's in my calculus class, so I assume that they are relevant, but we never attempted integrals that weren't explicitly defined. Any help would be much appreciated!

 

[jackmell]

The problem is as follows:

lim_{n\rightarrow\infty} \int^{1}_{0}√(1+n^{2}x^{2n})

My issue is that I'm unsure as to where to start. We just went over DE's in my calculus class, so I assume that they are relevant, but we never attempted integrals that weren't explicitly defined. Any help would be much appreciated!

How about start by analyzing the limit:

\lim_{n\to\infty} n^2 x^n,\quad 0<x<1