Let f : (-1,1) R be a continuous function. If _0^ x f(t) ,dt = 3 2 x, then f ( 3 2 ) is equal to:

JEE Main 2015 Mathematics question

Let be a continuous function. If , then is equal to:

Answer: (2)

Differentiate both sides with respect to , using the Leibniz rule on the left: the upper limit is , so

f( x)· x = .

To reach the required argument, choose so that , namely , for which

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Question ID VK-115397