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:

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