_ - 1 ^1 [x + [x + [x]]] , ,dx = (where [·] = greatest integer fu… - Vidyadip

MCQ

$\int\limits_{ - 1}^1 {[x + [x + [x]]]\,\,dx = } $ (where $[·] =$ greatest integer function)

A
$-1$
B
$-2$
✓
$-3$
D
$3$

✓

Answer

Correct option: C.

$-3$

c
$3 \int_{-1}^{1}[x] d x=3\left[\int_{-1}^{0}-1 d x+\int_{0}^{1} 0 d x\right]$

$=3[-x]_{-1}^{0}$

$=-3[0-(-1)]=-3$

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