JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \(f: R \rightarrow R\) be a function defined by \(f(x)=\left\{\begin{array}{l}\max \left\{t^{3}-3 t\right\} ; x \leq 2 \\ t \leq x \\ x^{2}+2 x-6 ; 2 < x < 3 \\ {[x-3]+9 ; 3 \leq x \leq 5} \\ 2 x+1 \quad ; \quad x > 5\end{array}\right\}\) 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 \(\left(3, \frac{27}{4}\right)\)
- B \(\left(3, \frac{23}{4}\right)\)
- C \(\left(4, \frac{27}{4}\right)\)
- D \(\left(4, \frac{23}{4}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(4, \frac{27}{4}\right)\)
Step-by-step Solution
Detailed explanation
\(\left\{\begin{array}{l} f ( x )= x ^{3}-3 x , x \leq-1 \\ 2,-1< x <2 \\ x ^{2}+2 x -6,2< x <3 \\ 9,3 \leq x <4 \\ 10,4 \leq x <5 \\ 11, x =5 \\ 2 x +1, x >5\end{array}\right.\) Clearly \(f ( x )\) is not differentiable at \(x =2,3,4,5 \Rightarrow m =4\)…
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