Arc Length Problem

 Posts: 47
 Joined: Mon Mar 22, 2010 2:42 am
Arc Length Problem
How to evaluate the length of arc of y=x^4/4 from on [0,a]? thanks.
Re: Arc Length Problem
The formula for arc length is
$$\int_0^a \sqrt{(1 + (\frac{dy}{dx})^2} dx$$
Sorry I edited it to simplify as you were posting!
$$\int_0^a \sqrt{(1 + (\frac{dy}{dx})^2} dx$$
Sorry I edited it to simplify as you were posting!
Last edited by origin415 on Fri Apr 09, 2010 8:20 am, edited 2 times in total.

 Posts: 47
 Joined: Mon Mar 22, 2010 2:42 am
Re: Arc Length Problem
I'm ok with this formula...but I'm stuck with the integral...so i want to ask for help, thanks.origin415 wrote:First you want to parametrize x and y, so
x(t) = t
y(t) = t^4/4
then the formula for arc length is
$$\int_0^a \sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2} dt$$
Re: Arc Length Problem
Well you can't actually do that integral, so don't try it (http://www.wolframalpha.com/input/?i=In ... %29%2Cx%29). What are the multiple choice answers? Maybe you can estimate the answer if the answers are not too close to one another.
If a is small, than $$\sqrt{1+x^6}$$ is close to 1, if a is large, its close to $$x^3$$.
If a is small, than $$\sqrt{1+x^6}$$ is close to 1, if a is large, its close to $$x^3$$.