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Compute the average value of the function on the interval

Compute the average value of

    \[ f(x) = x^2, \qquad a \leq x \leq b. \]


We compute the average A(f),

    \[ A(f) = \frac{1}{b-a} \int_a^b x^2 \, dx = \frac{b^3-a^3}{3 (b-a)} = \frac{b^2 + ab + a^2}{3}. \]

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