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Definite Integration question

2022 · 29 Jun · Shift 1 · Q22

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PYQ Library
JEE Main
Mathematics
Definite Integration
2022 · 29 Jun · Shift 1 · Q22

Definite Integration question

2022 · 29 Jun · Shift 1 · Q22

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let

f:R \to R

be a function defined by :

f(x) = \left\{ {\begin{matrix} {\max \,\{ {t^3} - 3t\} \,t \le x} & ; & {x \le 2} \\ {{x^2} + 2x - 6} & ; & {2 5} \\ \end{matrix} } \right.

where [t] is the greatest integer less than or equal to t. Let m be the number of points where f is not differentiable and

I = \int\limits_{ - 2}^2 {f(x)\,dx}

. Then the ordered pair (m, I) is equal to :

A
$\left( {3,\,{{27} \over 4}} \right)$
B
$\left( {3,\,{{23} \over 4}} \right)$
C
$\left( {4,\,{{27} \over 4}} \right)$
D
$\left( {4,\,{{23} \over 4}} \right)$

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