Integral Calculus: JEE Main 2022 Mathematics question

JEE Main 2022 · 29 Jun, Morning shift · Q3424

JEE Main 202229 Jun, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

Let

f:R \to R

be a function defined by :

f(x) = \left\{ {\matrix{ {\max \,\{ {t^3} - 3t\} \,t \le x} & ; & {x \le 2} \cr {{x^2} + 2x - 6} & ; & {2 < x < 3} \cr {[x - 3] + 9} & ; & {3 \le x \le 5} \cr {2x + 1} & ; & {x > 5} \cr } } \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 :

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JEE Main 2022 Integral Calculus Question with Solution (29 Jun Morning shift, Q3424) | JEE Arc

JEE Main 2022 · 29 Jun, Morning shift · Q3424

JEE Main 202229 Jun, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

Let

f:R \to R

be a function defined by :

f(x) = \left\{ {\matrix{ {\max \,\{ {t^3} - 3t\} \,t \le x} & ; & {x \le 2} \cr {{x^2} + 2x - 6} & ; & {2 < x < 3} \cr {[x - 3] + 9} & ; & {3 \le x \le 5} \cr {2x + 1} & ; & {x > 5} \cr } } \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 :