Correct answer is : 16
\(\mathrm{y}=\min \{\sin \mathrm{x}, \cos \mathrm{x}\}\)
\(\mathrm{x}\) - axis
\(\mathrm{x}-\pi \)
\( \mathrm{x}=\pi\)
\(\int_{0}^{\pi / 4} \sin \mathrm{x}=(\cos \mathrm{x})_{\pi / 4}^{0}=1-\frac{1}{\sqrt{2}}\)
\(\int_{-\pi}^{-3 \pi / 4}(\sin \mathrm{x}-\cos \mathrm{x})=(-\cos \mathrm{x}-\sin \mathrm{x})_{-\pi}^{-3 \pi / 4}\)
\(=(\cos \mathrm{x}+\sin \mathrm{x})_{-3 \pi / 4}^{-\pi}\)
\(=(-1+0)-\left(-\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}\right)\)
\(=-1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}\)
\(\int_{\pi / 4}^{\pi / 2} \cos x d x=(\sin x)_{\pi / 4}^{\pi / 2}=1-\frac{1}{\sqrt{2}}\)
\(\mathrm{A}=4\)
\(\mathrm{A}^{2}=16\)
