Question

${\int }_o^4${x}dx, where {.} denotes fractional part of x.

Answer 1

${\int }_0^4\left\{x\right\}dx$

$\left\{x\right\}=x-\left[x\right]$

you know,

$\left[2.3\right]=0.3$

$\left\{6\right\}=6-\left[6\right]=0$

$={\int }_0^4\left\{x\right\}dx$ Represent Area also

$=\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}=2$