# Thread: [SOLVED] Finding the arclength of a curve

1. ## [SOLVED] Finding the arclength of a curve

Hi I am having a problem finding the arclength of the function
f(x) = (1/3)(x^2 +2)^(3/2) x e [0,1]

I know the arclength formula but when I plug in the values I come down to:

ds = [integral from 0 to 1] underoot(1 + x^4 + 2x^2)dx

and can't figure out what to do from here, can you please show me steps on what to do next ?

thanks, EJ

2. Originally Posted by Cidious
Hi I am having a problem finding the arclength of the function
f(x) = (1/3)(x^2 +2)^(3/2) x e [0,1]

I know the arclength formula but when I plug in the values I come down to:

ds = [integral from 0 to 1] underoot(1 + x^4 + 2x^2)dx

and can't figure out what to do from here, can you please show me steps on what to do next ?

thanks, EJ
isn't it the formula is something like this?

$\displaystyle L = \int_a^b \sqrt{1 + \left[ f'(x) \right]^2} \, dx$

just do your integration..

3. kalagota, he actually did that, the problem is the integral:

$\displaystyle \int_0^1 {\sqrt {x^4 + 2x^2 + 1} \,dx} = \int_0^1 {\sqrt {\left( {x^2 + 1} \right)^2 } \,dx} = \int_0^1 {\left| {x^2 + 1} \right|\,dx} .$

Since $\displaystyle x^2+1>0,\,\forall\,x\in\mathbb R,$ we can remove the absolute value bars and just write $\displaystyle \int_0^1 {\left( {x^2 + 1} \right)\,dx},$ the rest is routine.

(Cidious see my signature for LaTeX typesetting.)