Let g(x)= _ 0 ^ x f(t) d t where f is such that 1 2 f(t) 1 for t [0,1] and 0 f(t) 1 2 for…
Mathematics · JEE Main · NTA Exams — Integral Calculus
Let \(g(x)=\int_{0}^{x} f(t) d t\) where f is such that \(\frac{1}{2} \leq f(t) \leq 1 \text { for } t \in[0,1]\) and \(0 \leq f(t) \leq \frac{1}{2} \text { for } t \in[1,2]\). Then, \(g(2)\) is contained in
- \(\left[-\frac{3}{2}, \frac{1}{2}\right)\)
- \([0,2)\)
- \(\left(\frac{3}{2}, \frac{5}{2}\right]\)
- \((2,4)\)
Answer
(C) ( 3 2 , 5 2 ]
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