What is the arc length of $f(x)=ln(x)/x$ on $x in [3,5]$ ?

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Answer 1 · 2015-11-08T23:13:25

You'll need some approximation techniques to get an answer.

$f'(x) = (1-lnx)/x^2$

So the arc length is given by:

$int_3^5 sqrt(1+(1-lnx)^2/x^4) dx$

The length is a bit more than $2$ . (According to Wolfram Alpha)

What is the arc length of f(x)=ln(x)/xf(x)=ln(x)/x on x in [3,5]x in [3,5]?