MathematicsMedium210×since 2002Q3463Let the function f:[0,2]→Rf:[0,2] \rightarrow \mathbb{R}f:[0,2]→R be defined as f(x)={emin{x2,x−[x]},x∈[0,1)e[x−logex],x∈[1,2]f(x)= \begin{cases}e^{\min \left\{x^{2}, x-[x]\right\},} & x \in[0,1) \\ e^{\left[x-\log _{e} x\right]}, & x \in[1,2]\end{cases}f(x)={emin{x2,x−[x]},e[x−logex],x∈[0,1)x∈[1,2] where [t][t][t] denotes the greatest integer less than or equal to ttt. Then the value of the integral \int_\limits{0}^{2} x f(x) d x is :A2e−12 e-12e−1B2e−122 e-\frac{1}{2}2e−21C1+3e21+\frac{3 e}{2}1+23eD(e−1)(e2+12)(e-1)\left(e^{2}+\frac{1}{2}\right)(e−1)(e2+21)Check answerSkip