Với $0<x<\pi$, ta có: $\sin x=\cos x \Leftrightarrow x=\dfrac{\pi}{4}$
Diện tích hình phẳng cần tìm là:
$S=\int\limits_0^{\pi}|\sin x-\cos x|dx$
$=\int\limits_0^{\frac{\pi}{4}}(\cos x-\sin x)dx+\int\limits_{\frac{\pi}{4}}^{\pi}(\sin x-\cos x)dx$
$=(\sin x+\cos x)\left|\begin{array}{l}\dfrac{\pi}{4}\\0\end{array}\right.+(-\cos x-\sin x)\left\{\begin{array}{l}\pi\\\dfrac{\pi}{4}\end{array}\right.$
$=2\sqrt2$