The area bounded by the curve \(y=\sin x+\cos x\) and the co-ordinate axis in the first quadrant is

\(\sqrt{2}-1\) \(\sqrt{2}\) \(\sqrt{2}+1\) \(1\)

\(\sqrt{2}\)

\(\begin{aligned}\text{Area}&=\int_{0}^{\frac{\pi}{2}}\cos xdx+\int_{\frac{\pi}{4}}^{\frac{\pi}{2}}(\sin x-\cos x)dx\\ &=\sqrt{2}\end{aligned}\)