Practicing Success
Practicing Success
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The value of $\int_0^{11}[x]^3.dx$, where [*] denotes the greatest integer function, is |
0 14400 2200 3025 |
3025 |
$\int_0^{11}[x]^3dx=\sum\limits_{r=0}^{10}\int_r^{r+1}[x]^3dx=\sum\limits_{r=0}^{10}\int_r^{r+1}r^3\,dx$ $=\sum\limits_{r=0}^{10}(r^3)=0^3 + 1^3 + 2^3 + ....+10^3$ $=(\frac{10.11}{2})^2=(55)^2=3025$ |
