Question

14．f（x）=$\left\{\begin{array}{l}{x^2}，x≤1\\ 2-x，x＞1\end{array}$，则$\int_{\;0}^{\;2}{f（x）dx}$=（　　）

• A． $\frac{3}{4}$
• B． $\frac{4}{5}$
• C． $\frac{5}{6}$
• D． $\frac{6}{7}$

Answer 1

分析 直接利用分段函数求解函数的定积分即可．

解答 解：f（x）=$\left\{\begin{array}{l}{x^2}，x≤1\\ 2-x，x＞1\end{array}$，则$\int_{\;0}^{\;2}{f（x）dx}$=${∫}_{0}^{1}{x}^{2}dx+{∫}_{1}^{2}（2-x）dx$=$\frac{1}{3}{x}^{3}{|}_{0}^{1}$+（2x-$\frac{1}{2}{x}^{2}$）${|}_{1}^{2}$=$\frac{5}{6}$．
故选：C．

点评 本题考查定积分的应用，考查计算能力．