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STD 12 - 7.2 definite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.2 definite integral4 Marks
Question
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.............
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Answer

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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