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