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Today's caluculation of integral 105

Source: Miyagi University of education entrance exam 1986

June 5, 2006
calculusintegrationfunctioncalculus computations

Problem Statement

Let a,ba,b be constant numbers such that 0<a<b.0<a<b. If a function f(x)f(x) always satisfies f′(x)>0f'(x) >0 at a<x<b,a<x<b, for a<t<ba<t<b find the value of tt for which the following the integral is minimized. ∫ab∣f(x)−f(t)∣x dx. \int_a^b |f(x)-f(t)|x\ dx.
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