For any natural number \( n \), the value of the integral \( \int_{0}^{\sqrt{n}}\left[x^{2}\righ...
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0For any natural number \( n \), the value of the integral \( \int_{0}^{\sqrt{n}}\left[x^{2}\right] d x \), is
(A) \( n \sqrt{n}+\sum_{r=1}^{n} \sqrt{r} \)
(B) \( n \sqrt{n}-\sum_{r=1}^{n} \sqrt{r} \)
(C) \( \sum_{r=1}^{n} \sqrt{r}-n \sqrt{n} \)
(D) none of these
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