The average value of \(f(x)=\dfrac{1}{x}\) from \(x=1\) to \(x=e\) is
\(\dfrac{1}{e+1}\)
\(\dfrac{1}{e-1}\)
\(\dfrac{1}{1-e}\)
\(e-1\)
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Approach
To find the average value:
$$ \frac{1}{e-1}\int\limits_1^e \frac{1}{x} dx $$ $$ = \frac{1}{e-1}\Big[\ln x \Big]_1^e $$ $$ = \frac{1}{e-1}(\ln e - \ln 1) $$ $$ = \frac{1}{e-1}(1-0) = \boxed{\frac{1}{e-1}} $$