Đáp án:
$\begin{array}{l}
\sin \left( {x + \dfrac{\pi }{4}} \right) = \dfrac{{ - \sqrt 2 }}{2}\\
\Leftrightarrow \left[ \begin{array}{l}
x + \dfrac{\pi }{4} = - \dfrac{\pi }{4} + k2\pi \\
x + \dfrac{\pi }{4} = \pi + \dfrac{\pi }{4} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = - \dfrac{\pi }{2} + k2\pi \\
x = \pi + k2\pi
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x = - \dfrac{\pi }{2}\\
x = \pi
\end{array} \right.\\
\Leftrightarrow S = \dfrac{{ - \pi }}{2} + \pi = \dfrac{\pi }{2}
\end{array}$
