Let fn(x) = \(\left\{\begin{array}{c} n^2 x, \quad 0 \leq x \leq \frac{1}{n} \\ -n^2 x+2 n, \quad \frac{1}{n} \leq x \leq \frac{2}{n} \text { on }[0,1] \\ 0, \quad \frac{2}{n} \leq x \leq 1 \end{array}\right.\)
then which of the following is true?
1
\(\rm\int_0^1\left(\displaystyle\lim _{n \rightarrow \infty} f_n(x)\right) d x=1\)
2
\(\rm \displaystyle\lim _{n \rightarrow \infty} \int_0^1 f_n(x) d x=0\)
3
fn(x) is uniformly convergent.
4
fn(x) is not uniformly convergent