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Q.
The area of the region bounded by the $Y$-axis, $y=\cos x$ and $y=\sin x, 0 \leq x \leq \frac{\pi}{2}$ is
Application of Integrals
Solution:
Let us first draw the graph of $\cos x$ and $\sin x$ between 0 to $\frac{\pi}{2}$ and shade the region bounded by them with $Y$-axis.
$\therefore$ Area of shaded region $=$ Area $(O A C B O-$ Area $(O C B O)$
$=\int\limits_0^\pi(\cos x-\sin x) d x$
$=[\sin x+\cos x]_0^{\pi / 4}$
$=\left[\left(\sin \frac{\pi}{4}+\cos \frac{\pi}{4}\right)-\{(\sin (0)+\cos (0)\}]\right.$
$=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-1=(\sqrt{2}-1)$ sq units
