105

Part of 2006 Today's Calculation Of Integral

Problems(1)

Today's caluculation of integral 105

Source: Miyagi University of education entrance exam 1986

a,b

be constant numbers such that

0<a<b.

f(x)

always satisfies

f'(x) >0

a<x<b,

a<t<b

find the value of

t

for which the following the integral is minimized.

\int_a^b |f(x)-f(t)|x\ dx.

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