Question

The area bounded by the curves y = sin x, y = cos x and y - axis in the first quadrant is

• A. $\sqrt{2}-1$
• B. $\sqrt{2}$
• C. $\sqrt{2}+1$
• D. None of these

Answer 1

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

$A={\int }_0^{\pi /4}\cos x-\sin xdxA={[\cos x+\sin x]}_0^{\pi /4}A=[\cos \left(\pi /4\right)+\sin \left(\pi /4\right)]-[\cos \left(0\right)+\sin \left(0\right)]A=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-1-0A=\sqrt{2}-1$