What is the arclength of $f(x)=sqrt((x-1)(2x+2))-2x$ on $x in [6,7]$ ?

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Answer 1 · 2018-06-02T16:25:18

$1.15037$

We have
$f(x)=sqrt((x-1)*2*(x+1))-2x$
$f(x)=sqrt(2)*sqrt(x^2-1)-2x$
So we get the integral

$int_6^7sqrt(1+(sqrt(2)*x/sqrt(x^2-1)-2)^2)dx$
With a numerical method we find
$approx 1.1.5037$

What is the arclength of f(x)=sqrt((x-1)(2x+2))-2xf(x)=sqrt((x-1)(2x+2))-2x on x in [6,7]x in [6,7]?