# Arc Lengths

• October 22nd 2009, 12:14 AM
superman69
Arc Lengths
Find the length of the curve defined by http://hosted.webwork.rochester.edu/...6934f23841.png from http://hosted.webwork.rochester.edu/...4e4e3fa271.png to http://hosted.webwork.rochester.edu/...655a5ac7d1.png.

Ok so first I know that we have to take the derivative which is Attachment 13472 And What would I do from then?
• October 22nd 2009, 12:17 AM
mr fantastic
Quote:

Originally Posted by superman69
Find the length of the curve defined by http://hosted.webwork.rochester.edu/...6934f23841.png from http://hosted.webwork.rochester.edu/...4e4e3fa271.png to http://hosted.webwork.rochester.edu/...655a5ac7d1.png.

Ok so first I know that we have to take the derivative which is Attachment 13472 And What would I do from then?

There are numerical errors in your derivative. After you have fixed them you should simplify the result, substitute it into the arclength formula (which I assume you have been taught) and then do the resulting integration.
• October 22nd 2009, 12:20 AM
superman69
Quote:

Originally Posted by mr fantastic
There are numerical errors in your derivative. After you have fixed them you should simplify the result, substitute it into the arclength formula (which I assume you have been taught) and then do the resulting integration.

Yes. But is this how you would set the equation Attachment 13473
• October 22nd 2009, 12:30 AM
superman69
Oh I see the mistake, 9 were suppose to be a 4
• October 22nd 2009, 12:36 AM
The Second Solution
Quote:

Originally Posted by superman69
Yes. But is this how you would set the equation Attachment 13473

Once you have made the necessary correction, the thing you are square rooting will simplify to $\left(\frac{x^2 + 16}{x^2 - 16}\right)^2$.
• October 22nd 2009, 12:38 AM
superman69
Quote:

Originally Posted by The Second Solution
Once you have made the necessary correction, the thing you are square rooting will simplify to $\left(\frac{x^2 + 16}{x^2 - 16}\right)^2$.

So this was what I got so far but I don't seem sure if this is correct
Attachment 13474
• October 22nd 2009, 01:59 AM
mr fantastic
Quote:

Originally Posted by superman69
So this was what I got so far but I don't seem sure if this is correct
Attachment 13474

Look, you need to get the derivative correct first. Please post your simplified answer for it and show all your working for how you got it.

Then ..... post #5 tells you what the $1 + \left( \frac{dy}{dx}\right)^2$ will simplify to.