1.
f:[0,2]Rf:[0,2]\to\mathbb{R}, f(x)={emin{x2,x[x]},x[0,1)exlogex,x[1,2]f(x)=\begin{cases}e^{\min\{x^2,x-[x]\}},&x\in[0,1)\\ e^{x-\log_e x},&x\in[1,2]\end{cases}. 02xf(x)dx\int_0^2 xf(x)dx is