Question:
If [.] represents the greatest integer function, then the value of
Solution:
$I=\int_{0}^{\sqrt{\pi / 2}}\left(\left[x^{2}\right]+[-\cos x]\right) d x$.
$=\int_{0}^{1} 0 \mathrm{dx}+\int_{1}^{\sqrt{\pi / 2}} \mathrm{dx}+\int_{0}^{\sqrt{\pi / 2}}(-1) \mathrm{dx}$
$=\sqrt{\frac{\pi}{2}}-1-\sqrt{\frac{\pi}{2}}=-1$
$\Rightarrow|\mathrm{I}|=1$
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