The area will be the shaded part. To calculate, divide into two parts, from (1) \(x=0\) to \(x=\frac{\pi}{4}\) and from (2) \(x=\frac{\pi}{4}\) to \(x=\frac{\pi}{2}\)

The first area is the area bounded by \(y = \sin x \) and the \(x -axis\) from \(x=0\) to \(x=\frac{\pi}{4}\) .

The second area is the area bounded by \(y = \cos x \) and the \(x -axis\) from \(x= \frac{\pi}{4}\) to \(x=\frac{\pi}{2}\).

\(A_1 = \int_{0}^{\frac{\pi}{4}} { \sin{x} ~dx} \)

\(A_1 =\cos {x} |_{0}^{\frac{\pi}{4}} \)

\(A_1 =| (\cos{\frac{\pi}{4}}) - (\cos {0} )|\)

\(A_1 = 0.293\)

\(A_2 = \int_{\frac{\pi}{4}}^{\frac{\pi}{2}} { \cos{x} ~dx} \)

\(A_2 = - \sin {x} |_{\frac{\pi}{4}}^{\frac{\pi}{2}} \)

\(A_2 =|- (\sin {\frac{\pi}{2}} ) + (\sin {\frac{\pi}{4}} )|\)

\(A_2 = 0.293\)

Answer: \(A = 0.293 +0.293 = 0.586~\text{sq area}\)