Length of a curve

**MathNeedy18** · December 10th 2007, 02:48 PM

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

.

**TKHunny** · December 10th 2007, 03:33 PM

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.

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