# Thread: any example for convergence of integral

1. ## any example for convergence of integral

fn,f are all continuous on [0,1]
$f_{n}(x) \longrightarrow f(x)$ pointwisely
and
$\int_{0}^{1}{f_{n}(x)}\longrightarrow\int_{0}^{1}{ f(x)}$

any example that fn does not converge uniformly to f ?

2. Look at $f_n(x)=\frac{x}{n}$. This converges to 0, but not uniformly. Additionally $\int f_n dx=\frac{1}{2n}\longrightarrow 0$