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Area Under the Curves question

2023 · 29 Jan · Shift 1 · Q36

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PYQ Library
JEE Main
Mathematics
Area Under the Curves
2023 · 29 Jan · Shift 1 · Q36

Area Under the Curves question

2023 · 29 Jan · Shift 1 · Q36

JEE MainMathematicsArea Under the CurvesMCQ+4 / −1

Let

[x]

denote the greatest integer

\le x

. Consider the function

f(x) = \max \left\{ {{x^2},1 + [x]} \right\}

. Then the value of the integral

\int\limits_0^2 {f(x)dx}

is

A
${{5 + 4\sqrt 2 } \over 3}$
B
${{4 + 5\sqrt 2 } \over 3}$
C
${{8 + 4\sqrt 2 } \over 3}$
D
${{1 + 5\sqrt 2 } \over 3}$

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