Let f: (0, 1) R be the function defined as f(x) = n if x [ 1 n+1 , 1 n ) where n N . Let g: (0, 1) R be a function such that _ x^2 ^ x 1-t t ,dt < g(x) < 2 x for all x (0, 1). Then _ x 0 f(x)g(x)

JEE Advanced 2023 Mathematics question

Let be the function defined as if where . Let be a function such that for all . Then

Answer: (C)

For : , so as (). For the lower bound,

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Question ID VK-034065