# Help please. arc length of the curve

• Dec 17th 2012, 05:10 AM
Oneztwo
Help please. arc length of the curve
So I have final coming up with week and I'm going through the review then I ran into this problem I just don't know what to do (for this particular problem, I understand the concept thou) so any help would be much appreciated. Thank you in advance. Oh and I'm a new user. Nice to meet you all.
• Dec 17th 2012, 05:27 AM
MarkFL
Re: Help please. arc length of the curve
I would begin by computing:

$\frac{dy}{dx}=7x^{\frac{5}{2}}$

thus:

$\sqrt{1+\left(\frac{dy}{dx} \right)^2}=\sqrt{1+\left(7x^{\frac{5}{2}} \right)^2}=\sqrt{1+49x^5}$

The arc-length is then:

$s=\int_0^{\frac{48}{49}}\sqrt{1+49x^5}\,dx$

At this point, I would use a numeric technique to get a decimal approximation.
• Dec 17th 2012, 06:19 AM
Oneztwo
Re: Help please. arc length of the curve
That's as far as I got I'm stuck trying to manipulate this. Tried the u substitution and all. Nothing works for me. Any additional help is appreciated. Ps. Thank you for the reply mark.