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Compute the average value of the function on the interval

Compute the average value of

    \[ f(x) = x^{1/2}, \qquad 0 \leq x \leq 4. \]


We compute the average A(f),

    \[ A(f) = \frac{1}{4} \int_0^4 x^{1/2} \, dx = \frac{1}{4}\cdot  \frac{2}{3}\cdot \left( x^{3/2} \biggr \rvert_0^4 \right) = \frac{1}{6} \cdot 8 = \frac{4}{3}. \]

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