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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
If $[.]$ represents the greatest integer function, then the value of $\int_{0}^{\sqrt{\pi / 2}}\left(\left[ x ^{2}\right]+[-\cos x ]\right) d x$ is.............
  • A
    $3$
  • B
    $6$
  • C
    $4$
  • ✓
    $1$
✓

Answer

Correct option: D.
$1$
d
$I =\int_{0}^{\sqrt{\pi / 2}}\left(\left[ x ^{2}\right]+[-\cos x ]\right) d x$

$=\int_{0}^{1} 0 dx +\int_{1}^{\sqrt{\pi / 2}} d x +\int_{0}^{\sqrt{\pi / 2}}(-1) d x$

$=\sqrt{\frac{\pi}{2}}-1-\sqrt{\frac{\pi}{2}}=-1$

$\Rightarrow| I |=1$

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