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$4$
- ✓$1$
$=\int_{0}^{1} 0 dx +\int_{1}^{\sqrt{\pi / 2}} d x +\int_{0}^{\sqrt{\pi / 2}}(-1) d x$
$=\sqrt{\frac{\pi}{2}}-1-\sqrt{\frac{\pi}{2}}=-1$
$\Rightarrow| I |=1$
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and $g(x)=\left(x-\frac{1}{2}\right)^{2}, x \in R .$ Then the area (in sq. units) of the region bounded by the curves, $y=f(x)$ and $y=g(x)$ between the lines, $2 \mathrm{x}=1$ and $2 \mathrm{x}=\sqrt{3},$ is