If [.] represents the greatest integer functi | vedclass

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(C) Let $I = \int_{0}^{\sqrt{\pi / 2}} ([x^2] + [-\cos x]) dx$. Since $0 \le x \le \sqrt{\pi / 2} \approx 1.25$,we have $0 \le x^2 \le \pi / 2 \approx

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$-1$

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(C) Let $I = \int_{0}^{\sqrt{\pi / 2}} ([x^2] + [-\cos x]) dx$. Since $0 \le x \le \sqrt{\pi / 2} \approx 1.25$,we have $0 \le x^2 \le \pi / 2 \approx 1.57$. Thus,$[x^2] = 0$ for $0 \le x For $0 \le x \le \sqrt{\pi / 2}$,we have $0 \le \cos x \le 1$. Specifically,for $x \in (0, \sqrt{\pi / 2}]$,$0 \le \cos x Thus,$[-\cos x] = -1$ for $x \in (0, \sqrt{\pi / 2}]$ and $[-\cos x] = 0$ at $x = 0$. $I = \int_{0}^{1} (0 - 1) dx + \int_{1}^{\sqrt{\pi / 2}} (1 - 1) dx = \int_{0}^{1} (-1) dx + 0 = -1$.

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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