Question

$\underset{0}{\overset{1}{\int }}\left\{x\right\}dx,$ where {x} denotes the fractional part of x.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ I=\underset{0}{\overset{1}{\int }}\left\{x\right\}dx \\ \mathrm{We}\mathrm{know}\left\{x\right\}=x,0<x<1 \\ \therefore I=\underset{0}{\overset{1}{\int }}xdx \\ ={\left[\frac{x^2}{2}\right]}_0^1 \\ =\frac{1}{2}-\frac{0}{2} \\ =\frac{1}{2} \end{gathered}$$
s 4430. →