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Today's calculation of Integral 617

Source:

July 1, 2010
calculusintegrationfunctioncalculus computations

Problem Statement

Let y=f(x)y=f(x) be a function of the graph of broken line connected by points (−1, 0), (0, 1), (1, 4)(-1,\ 0),\ (0,\ 1),\ (1,\ 4) in the xx -yy plane. Find the minimum value of ∫−11{f(x)−(a∣x∣+b)}2dx.\int_{-1}^1 \{f(x)-(a|x|+b)\}^2dx.
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