MathNet 2016-part-03 — 184 problems (EN–VI) Question 165

Consider $I_{n} = \int_{0}^{4} \sqrt[n]{x^{n} + (4-x)^{n}} \, dx$, $n \in \mathbb{N}$, $n \geq 2$. Compute $\lim_{n \rightarrow \infty} I_{n}$.