# Calculust 5

Calculus Level 5

$\large \lim_{n\to\infty} \dfrac{1}{n^2} \sum\limits_{k=0}^{n-1} \left( k \int_{k}^{k+1} \sqrt{(x-k)(k+1-x)} \, dx \right)$

The above expression can be represented as $$\dfrac{\pi}{a}$$, then what is $$a$$?

×