1. ## Arc Lengths

Find the length of the curve defined by from to .

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

2. Originally Posted by superman69
Find the length of the curve defined by from to .

Ok so first I know that we have to take the derivative which is 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.

3. 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

4. Oh I see the mistake, 9 were suppose to be a 4

5. Originally Posted by superman69
Yes. But is this how you would set the equation
Once you have made the necessary correction, the thing you are square rooting will simplify to $\displaystyle \left(\frac{x^2 + 16}{x^2 - 16}\right)^2$.

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

So this was what I got so far but I don't seem sure if this is correct

7. Originally Posted by superman69
So this was what I got so far but I don't seem sure if this is correct
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 $\displaystyle 1 + \left( \frac{dy}{dx}\right)^2$ will simplify to.