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\int_{0}^{1} a^{k} x^{k} d x =

MathematicsDefinite IntegrationAP EAMCETAP EAMCET 2022 (04 Jul Shift 1)

Options:

A $\lim_{n \to \infty} \frac{a^{k} (1 + 2^{k} + 3^{k} \dots + n^{k})}{n^{k + 1}}$
B $\lim_{n \to \infty} \frac{a^{k} + a^{k} + \dots + a^{k}}{n^{k + 1}}$
C $\lim_{n \to \infty} \frac{1}{n} \sum {(\frac{r}{n})}^{k}$
D $\lim_{n \to \infty} \frac{1}{n} \sum {(\frac{2 r}{n})}^{k}$