Question

$\underset{0}{\overset{\mathrm{\pi }/2}{\int }}\left(\sin x+\cos x\right)dx$

Answer 1

$$\begin{gathered} \mathrm{Let}I={\int }_0^{\frac{\mathrm{\pi }}{2}}\left(\sin x+\cos x\right)\mathit{d}x.\mathrm{Then}, \\ I={\left[-\cos x+\sin x\right]}_0^{\frac{\mathrm{\pi }}{2}} \\ \Rightarrow I=0+1-\left(-1+0\right) \\ \Rightarrow I=2 \end{gathered}$$