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STD 12 - 7.2 definite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.2 definite integral1 Mark
MCQ
$\int\limits_a^b {} \, [x] \,dx + \int\limits_a^b {} \, [ - x] \,dx$

where $[. ]$ denotes greatest integer function is equal to :

  • A
    $a + b$
  • B
    $b - a$
  • ✓
    $a - b$
  • D
    $\frac{{a\, + \,b}}{2}$
✓

Answer

Correct option: C.
$a - b$
c
$[x] + [- x] = \left[ {\begin{array}{*{20}{c}}{0\,\,\,\,if\,\,\,\,x\,\, \in \,\,I\,\,\,}\\{ - \,1\,\,\,\,if\,\,\,\,x\,\, \notin \,\,I}\end{array}} \right.$

$\Rightarrow$ $I = \int\limits_a^b {}  - dx = a - b$

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