2. If $\sin x+\cos x=\frac{\sqrt{2}}{2}$, then $\sin ^{3} x+\cos ^{3} x=$ $\qquad$
2. $\frac{5 \sqrt{2}}{8}$.

Notice,
$$
\begin{array}{l}
\sin x \cdot \cos x=\frac{(\sin x+\cos x)^{2}-1}{2}=-\frac{1}{4} \text {. } \\
\text { Then } \sin ^{3} x+\cos ^{3} x \\
=(\sin x+\cos x)^{3}-3 \sin x \cdot \cos x(\sin x+\cos x) \\
=\frac{\sqrt{2}}{4}+\frac{3 \sqrt{2}}{8}=\frac{5 \sqrt{2}}{8} .
\end{array}
$$