Problem

甲、填充題：共 8 題，每題 8 分，共 64 分。請在答案卷上列出題號依序作答。

8. Suppose $f''$ is continuous on $[0,1]$, $f(1)=2$, $f'(1)=2$ and the average value of $f$ on $[0,1]$ is $2$. Evaluate $\displaystyle\int_0^1 x^2f''(x)\,dx$. Answer : \underline{\quad(1)\quad}