Let f: R R be a differentiable function such that f(0)=0, f ( 2 )=3 and f'(0)=1. If g(x)= _x^ 2 [f'(t) cosec t- t cosec t ,f(t)] ,dt for x (0, 2 ], then _ x 0 g(x)=

JEE Advanced 2017 Mathematics question

Let be a differentiable function such that , and . If

g(x)=[f'(t)\operatorname{cosec}t- t\operatorname{cosec}t f(t)] dt

for , then

Answer: 2

The integrand is (product rule, since ). So

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Question ID VK-026636