$$
\begin{aligned}
&\text { 设 } a < 0 < b, f(x) \text { 在 }[a, b] \text { 上二阶导函数连续. 求证: } \exists \xi \in(a, b) \text {, 使得 }\\
&\int_a^b f(x) d x=b f(b)-a f(a)-\frac{1}{2}\left[b^2 f^{\prime}(b)-a^2 f^{\prime}(a)\right]+\frac{1}{6}\left(b^3-a^3\right) f^{\prime \prime}(\xi) .
\end{aligned}
$$