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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
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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