Question

20．计算$\int_0^2$f（x）dx，其中，f（x）=$\left\{\begin{array}{l}2x\begin{array}{l}，{0≤x＜1}\end{array}\\ 5\begin{array}{l}，{\begin{array}{l}{\;\;\;1≤x≤2．}{\;}\end{array}}\end{array}\end{array}$．

Answer 1

分析 根据分段函数的积分公式进行计算即可．

解答 解：∵f（x）=$\left\{\begin{array}{l}2x\begin{array}{l}，{0≤x＜1}\end{array}\\ 5\begin{array}{l}，{\begin{array}{l}{\;\;\;1≤x≤2．}{\;}\end{array}}\end{array}\end{array}$
∴$\int_0^2$f（x）dx=∫${\;}_{0}^{1}$2xdx+∫${\;}_{1}^{2}$5dx=x²|${\;}_{0}^{1}$+5x|${\;}_{1}^{2}$=1-0+5（2-1）=1+5=6．

点评 本题主要考查积分的计算，根据分段函数的积分公式是解决本题的关键．比较基础．