Question

Consider the curves $y=\sin x$ and $y=\cos x$.

What is the area of the region bounded by the above two curves and the lines $x=0$ and $x=\frac{\pi }{4}$?

• A. $\sqrt{2}-1$
• B. $\sqrt{2}+1$
• C. $\sqrt{2}$
• D. $2$

Answer 1

The correct option is A $\sqrt{2}-1$

The area enclosed by $y=sinx,y=cosx,x=0,x=\frac{\pi }{4}$ is given by

${\int }_0^{\frac{\pi }{4}}(\cos x-\sin x)dx$

$=|\sin x+\cos x{|}_0^{\frac{\pi }{4}}$

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

$=\sqrt{2}-1$