# Length of a line

• Sep 30th 2009, 01:12 PM
binomialbrother
Length of a line
Hi there, i was puzzling over this today and wonder if someone could help.

if i had a line of some equation, say

$y=3(x^3)+2(x^2)+x+1$

which is just some cubic, how would i calculate the length of a line between say, 0 and 5? obviously i would have to use integration by substitution, but where do i go from there?

thanks
• Sep 30th 2009, 01:20 PM
pomp
Sorry I don't quite understand what you mean by where do i go from there, but this is the formula for calculating the length s of the path from x=a to x=b of a continuous and continuously differentiable function f(x):

$s = \int_a^b \sqrt{1 + f'(x)^2} dx$ .
• Oct 1st 2009, 10:52 PM
binomialbrother
thanks, that was helpful. i hadn't been able to find a concise approach online.