If [.] represents the greatest integer function, then the value o… - Vidyadip

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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