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Definite Integration question

2023 · 11 Apr · Shift 2 · Q35

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JEE Main
Mathematics
Definite Integration
2023 · 11 Apr · Shift 2 · Q35

Definite Integration question

2023 · 11 Apr · Shift 2 · Q35

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let the function

f:[0,2] \rightarrow \mathbb{R}

be defined as

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}

where

[t]

denotes the greatest integer less than or equal to

t

. Then the value of the integral

\int_{0}^{2} x f(x) d x

is :

A
$2 e-1$
B
$2 e-\frac{1}{2}$
C
$1+\frac{3 e}{2}$
D
$(e-1)\left(e^{2}+\frac{1}{2}\right)$

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