Question

The value of $I={\int }_{-1}^1\left[xsin(\pi x)\right]dx$ is (where [·] denotes the greatest integer function)

• A. $\pi$
• B. $2\pi$
• C. $0$
• D. $-\pi$

Answer 1

Answer: (C)

$I=2{\int }_0^1\left[xsin(\pi x)\right]dx$
Now, $xsin(\pi x)\in \left(0,1\right)$
as $x\in \left(0,1\right)$
$\therefore \left[xsin(\pi x)\right]=0$
$\therefore I=2{\int }_0^{1}0dx=0$