Definite Integration

Home Forums Math Olympiad, I.S.I., C.M.I. Entrance Definite Integration

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    Lavisha Sharma
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    Consider continuous functions on the interval [0,1] which statisfy the following two conditions:

    i) f (x) <= (5)^(1/2) for all belonging to [0,1]

    ii)  f (x) <= 2/x for all x belonging to [0, 1/2]

    Then, the smallest real number a such that the inequality integration of f(x)dx running from 0 to 1 , is less than equal to a.

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