Question

The value of the integral ${\int }_0^{0.9}[x-2[x\left]\right]dx$, where $[\cdot ]$ denotes the greatest integer function, is?

• A. $0.9$
• B. $0$
• C. $1.8$
• D. $-0.9$

Answer 1

Answer: (B)

$0$

${\int }_0^{0.9}[x-2[x\left]\right]dx$
$={\int }_0^{0.9}[x-2\times 0]dx$
$={\int }_0^{0.9}\left[x\right]dx={\int }_0^{0.9}0dx=0$.