What is the arclength of $f(x)=sqrt((x-1)(x+2)-3x$ on $x in [1,3]$ ?

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Answer 1 · 2016-01-15T10:37:53

$s=1.04487$ if we compute from $x=(1+sqrt(3))$ to $x=3$

there is no such length from $x=1$ to $x=3$

observe the graph $f(x)=sqrt((x-1)(x+2)-3x)$
graph{sqrt((x-1)(x+2)-3x) [-5, 5, -2.5, 2.5]}

the possible length is from $x=(1+sqrt(3))$ to $x=3$ and not from $x=1$ to $x=3$

$y'=(x-1)/sqrt(x^2-2x-2)$

$s=int_(1+sqrt(3))^3 sqrt(1+((x-1)/sqrt(x^2-2x-2))^2$

What is the arclength of f(x)=sqrt((x-1)(x+2)-3xf(x)=sqrt((x-1)(x+2)-3x on x in [1,3]x in [1,3]?