Let the function $f :[0,2] \rightarrow R$ be defined as
$f(x)=\left\{\begin{array}{cc}e^{\min \left[x^2, x-[x]\right\}}, & x \in[0,1) \\e^{\left[x-\log _e x\right]}, & x \in[1,2]\end{array}\right.$
where [t] denotes the greatest integer less than or equal to $t$. Then the value of the integral $\int \limits_0^2 x f(x) d x$ is
Let the function $f :[0,2] \rightarrow R$ be defined as
$f(x)=\left\{\begin{array}{cc}e^{\min \left[x^2, x-[x]\right\}}, & x \in[0,1) \\e^{\left[x-\log _e x\right]}, & x \in[1,2]\end{array}\right.$
where [t] denotes the greatest integer less than or equal to $t$. Then the value of the integral $\int \limits_0^2 x f(x) d x$ is
- [JEE MAIN 2023]
- A
$2 e -1$
- B
$1+\frac{3 e }{2}$
- C
$2 e -\frac{1}{2}$
- D
$(e-1)\left(e^2+\frac{1}{2}\right)$
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