Calculust 5

Calculus Level 4

limn1n2k=0n1(kkk+1(xk)(k+1x)dx)\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 πa \dfrac{\pi}{a} , then what is aa?

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