What is the arclength of $f(x)=arctan(2x)/x$ on $x in [2,3]$ ?

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Answer 1 · 2018-06-06T16:39:18

$1.01941$

Differentiaitng
$f(x)=arctan(2x)/x$ with respect to $x$
we get

$f'(x)=2/(x(1+4x^2))-arctan(2x)/x^2$
so we have to solve the integral
$int_2^3sqrt(1+(2/(x*(1+4x^2))-arctan(2x)/x^2)^2)dxapprox 1.01941$

What is the arclength of f(x)=arctan(2x)/xf(x)=arctan(2x)/x on x in [2,3]x in [2,3]?