Question

Find the area bounded by the curve $y=\cos x,y=\sin x$, y-axis and $0\le x\le \frac{\pi }{4}$

Answer 1

Area bounded $={\int }_0^{\frac{\pi }{4}}(\cos x-\sin x)dx=[\sin x+\cos x{]}_0^{\frac{\pi }{4}}$

$=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-0-1$

$=\sqrt{2}-1$