2. If $\sin x+\cos x=$ $\frac{\sqrt{2}}{2}$, then $\sin ^{3} x+\cos ^{3} x=$ $\qquad$
$$
(\sin x+\cos x)^{2}=1+2 \sin x \cos x=\frac{1}{2} \Rightarrow \sin x \cos x=-\frac{1}{4} \text {, }
$$

So $\sin ^{3} x+\cos ^{3} x=(\sin x+\cos x)(1-\sin x \cos x)=\frac{\sqrt{2}}{2} \cdot \frac{5}{4}=\frac{5 \sqrt{2}}{8}$.