Limit of norms

Let $a,b \in \mathbb{R}$ such that $a<b$ and $f\in C^0([a,b],\R_+)$, what is $\displaystyle\lim_{n\rightarrow \infty}\left(\int_{a}^{b}(f(x))^{n}dx\right)^{\frac{1}{n}}$?