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The average value of a function \( f(x) \) over the interval, \( [a, b] \) is the number
\[
\mu=\frac{1}{b-a} \int_{a}^{b} f(x) d x
\]
The square root \( \left\{\frac{1}{b-a} \int_{a}^{b}[f(x)]^{2} d x\right\}^{1 / 2} \) is called the root mean square of \( f \) on \( [a, b] \). The average value \( \mu \) is attained if \( f \) is continuous on \( [a, b] \).
The average value of pressure varying from 2 to 10 atm if the pressure \( p \) and the volume \( v \) are related by \( p v^{3 / 2}=160 \) is
(a) \( \frac{20}{\sqrt[3]{20}(\sqrt[3]{10}+\sqrt[3]{2})} \)
(b) \( \frac{10}{\sqrt[3]{10}+\sqrt[3]{2}} \)
(c) \( \frac{40}{\sqrt[3]{20}(\sqrt[3]{10}+\sqrt[3]{2})} \)
(d) \( \frac{160}{\sqrt[3]{20}(\sqrt[3]{10}+\sqrt[3]{2})} \)
\( \mathrm{P} \)
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