Question

Let [x] stands for the greatest integer function. The value of $\int_{0}^{21}{\lbrack x\rbrack^{3}}$dx is -

• A. 44001
• B. 44000
• C. 40400
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

$\int_{0}^{21}{\lbrack x\rbrack^{3}dx}$ = $\sum_{r = 0}^{20}{\int_{r}^{r + 1}{\lbrack x\rbrack^{3}dx}}$

$\sum_{r = 0}^{20}{\int_{r}^{r + 1}{r^{3}dx}}$

=$\sum_{1}^{20}{r^{3} = \left( \frac{20.21}{2} \right)^{2}}$ = 44100