Question

${\int }_0^{5/2}(\left[x\right]+[-x])dx$ equals

• A. $\frac{5}{2}$
• B. $-\frac{5}{2}$
• C. $\frac{7}{2}$
• D. none of these

Answer 1

The correct option is B $-\frac{5}{2}$

(i) $\left[x\right]+[-x]=0,x\in I$

(ii) $\therefore I={\int }_0^1\left[x\right]+[-x]dx+{\int }_0^2\left[x\right]+[-x]dx+{\int }_2^{5/2}\left[x\right]+[-x]$

$=-{\int }_0^{1}dx-{\int }_1^{2}dx-{\int }_2^{5/2}dx$

$=-[1+(2-1)+(\frac{5}{2}-2)]=\frac{-5}{2}$