Let the function {\f}:[0,2] \to R be defined as f(x)={\\begin{array}{cc}e^{\min \{x^2 & x-[x]\\end{array} }, , x \in[0,1) ; e^{ [x-\log _c x] }, , x \in[1,2) }. where [t] denotes the greatest integer less than or equal to t. Then the value of the integral \int_{0}^{2} x f(x) \dx is [11-Apr-2023 shift 2]

Correct Answer is : (e−1)(e2+12)

( {\e}-1) ( {\e}^2+\frac{1}{2})

JEE Mains 11-Apr-2023 Shift 2 Solved Paper

Section: Mathematics

Question : 17 of 90

Marks: +1, -0

Let the function f:[0,2]→R be defined as
f(x)={

emin{x2,x−[x]}	‌	x∈[0,1)
e[x−logcx]	‌	x∈[1,2)

.
where [t] denotes the greatest integer less than or equal to t. Then the value of the integral

∫

xf(x)‌dx is

[11-Apr-2023 shift 2]

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