Mathematics, 15.07.2019 00:20 isabellajmoody
Find the average value of f(x) = 1/x over the interval [e, 2e]. ln(2)/e -1/2e^ ln2 ln3
Answers: 2
![\bf \displaystyle \cfrac{1}{2e-e}\int_{e}^{2e}~\cfrac{1}{x}\cdot dx\implies \left. \cfrac{1}{e}\cdot ln(x) \right]_{e}^{2e}\implies \left[ \cfrac{ln(2e)}{e} \right]-\left[ \cfrac{ln(e)}{e}\right] \\\\\\ \left[ \cfrac{ln(2)+ln(e)}{2e} \right]-\left[ \cfrac{1}{e} \right]\implies \cfrac{ln(2)}{e}+\cfrac{ln(e)}{e}-\cfrac{1}{e}\implies \cfrac{ln(2)}{e}+\cfrac{1}{e}-\cfrac{1}{e} \\\\\\ \cfrac{ln(2)}{e}](/tpl/images/0090/5186/f7d05.png)
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Find the average value of f(x) = 1/x over the interval [e, 2e]. ln(2)/e -1/2e^ ln2 ln3...
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