# Math Help - Length of a curve

1. ## Length of a curve

I am using this formula: sqrt((f'(x))^2+((g'(x)^2)) dx...Is that right? Because I keep getting weird answers that are too big! HELP!!!!

Find the length of the curve defined by

from to .

2. What formula is that? It's a single function of a single variable. Where did you get two functions?

Let's see

$f(x)\;=\;4*x^{3/2}\;+\;3$

$f'(x)\;=\;6*x^{1/2}$

$\int_{5}^{8}\left(\sqrt{1\;+\;(6*x^{1/2})^{2}}\right)\;dx$. You should be able to do that.

I get $\frac{1}{54}*(4913\;-\;181\sqrt{181})\;\approx\;45.887$

A quick look at the graph shows f(x) isn't far from straight on [5,8], so a rough estimate shows $\sqrt{44^{2}+3^{2}}=44.10$. I believe it.