Let f : R R be a differentiable function such that f( /4) = 2 , f( /4) = 0 and f'( /2) = 1 and let g(x) = _ x ^ /4 (f'(t) sec t + tan t sec t f(t))dt for x [ /4, /2). Then _ x ( /2)^ - g(x) is equal to

JEE Main 2022 Mathematics question

Let f : be a differentiable function such that , and and let sec t + tan t sec t f(t))dt for x , ). Then g(x) is equal to

Answer: (2)

The integrand is d/dt[f(t) sec t], so g(x) = [f(t) sec sec x = 2 − f(x)/cos x. As (with

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Question ID VK-034872