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 .
What formula is that? It's a single function of a single variable. Where did you get two functions?
Let's see
$\displaystyle f(x)\;=\;4*x^{3/2}\;+\;3$
$\displaystyle f'(x)\;=\;6*x^{1/2}$
$\displaystyle \int_{5}^{8}\left(\sqrt{1\;+\;(6*x^{1/2})^{2}}\right)\;dx$. You should be able to do that.
I get $\displaystyle \frac{1}{54}*(4913\;-\;181\sqrt{181})\;\approx\;45.887$
A quick look at the graph shows f(x) isn't far from straight on [5,8], so a rough estimate shows $\displaystyle \sqrt{44^{2}+3^{2}}=44.10$. I believe it.