$\lim_{n\to\infty}\int_{0}^{\sqrt{n}}\left(1-\frac{\left x^2\right}{n}\right )^{n}dx$

i couldn't tackle it
thanks for now.

2. Re: a problem about integral

Do you know the dominated convergence theorem?

3. Re: a problem about integral

It can be useful the substitution $t=x/\sqrt{n}$, so $\int_{0}^{\sqrt{n}}(1-x^2/n)^n\;dx=\sqrt{n}\int_{0}^{1}(1-t^2)^n\;dt$ .