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If $ f_{ave} [a, b] $ denotes the average value of $ f $ on the interval $ [a, b] $ and $ a < c < b $, show that

$$ f_{ave} [a, b] = \frac{c - a}{b - a} f_{ave} [a, c] + \frac{b - c}{b - a} f_{ave} [c, b] $$

$f_{a v e}[a, b]$

Applications of Integration

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