# Length of a curve

• Dec 6th 2010, 08:22 AM
snopy
Length of a curve
Hi, I need calculate the length of a curve. Could someone help me please?

Formula:

http://www.sdilej.eu/pics/876126889a...ec1106c34.jpeg
• Dec 6th 2010, 08:26 AM
Ackbeet
Well, what have you tried so far?
• Dec 6th 2010, 09:20 AM
snopy
I can not derivative and exponentiate: (
• Dec 6th 2010, 09:31 AM
Ackbeet
You can't differentiate your function? Differentiation is like an onion: you have to peel back the layers, in inverse order in which you would compute. Let's say you take your function

$f(x)=\dfrac{1}{3}(x-3)\sqrt{x},$

and you want to find $f(3).$ List all the computations you must do, in order, in order to find this value.
• Dec 6th 2010, 09:47 AM
snopy
• Dec 6th 2010, 09:49 AM
Ackbeet
No, I'm afraid your differentiation is incorrect. What differentiation rule do you have to use here?
• Dec 6th 2010, 11:24 AM
HallsofIvy
Try writing $y= \frac{1}{3}(x- 3}\sqrt{x})$ as $y= \frac{1}{3}(x- 3)x^{1/2}= \frac{1}{3}x^{3/2}- \frac{1}{3}x^{1/2}$.