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Today's calculation of integral 526

Source: 1972 Tokyo Institute of Technology entrance exam, Problem 4

January 10, 2010
calculusintegrationfunctioncalculus computations

Problem Statement

For a function satisfying f′(x)>0 f'(x) > 0 for a≤x≤b a\leq x\leq b, let F(x) \equal{} \int_a^b |f(t) \minus{} f(x)|\ dt. For what value of x x is F(x) F(x) is minimized?
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