The value of $\int_0^{11}[x]^3.dx$, where [*] denotes the greatest integer function, is
Answer & explanation
Correct answer: option 4
$\int_0^{11}[x]^3dx=\sum\limits_{r=0}^{10}\int_r^{r+1}[x]^3dx=\sum\limits_{r=0}^{10}\int_r^{r+1}r^3\,dx$
$=\sum\limits_{r=0}^{10}(r^3)=0^3 + 1^3 + 2^3 + ....+10^3$
$=(\frac{10.11}{2})^2=(55)^2=3025$