How to find $\lim_{n \rightarrow \infty } \sqrt[n]{ \int_0^1 |f(x)|^{n} dx } $?
Finding $\lim\limits_{n \rightarrow \infty}\left(\int_0^1(f(x))^n\,\mathrm dx\right)^\frac{1}{n}$ for continuous $f:[0,1]\to[0,\infty)$