If [.] represents the greatest integer function the value of ∫0π/2x2−cosxdx is .........

I=∫0π2x2+−cosxdx∫010dx+∫1π2dx+∫0π2−1dx=π2−1+π2=−1I=−1=1

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If [.] represents the greatest integer function the value of $|\int_{0}^{\sqrt{π / 2}} [[x^{2}] - \cos x] d x|$ is .........

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$I = \int_{0}^{\sqrt{\frac{π}{2}}} [x^{2}] + [- \cos x] d x$

$\int_{0}^{1} 0 d x + \int_{1}^{\sqrt{\frac{π}{2}}} d x + \int_{0}^{\sqrt{\frac{π}{2}}} - 1 d x$

$= \sqrt{\frac{π}{2}} - 1 + \sqrt{\frac{π}{2}} = - 1$

$|I| = |- 1| = 1$

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