Q. The area of the region bounded by Y-axis, y = cos x and y = sin x 0 $\le$ x $\le \frac{\pi}{2}$ is

Solution:

$Required\, area =\int\limits_{0}^{\frac{\pi}{4}}\left(cos\,x-sin\,x\right)dx$
$=\left(sin\,x+cos\,x\right)_{0}^{\frac{\pi}{4}}$
$=\left(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-1\right)$
$=\left(\sqrt{2}-1\right) sq \, units$

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