# Thread: Arc Length of Curve!

1. ## Arc Length of Curve!

What is the arc length of the part of the curve y= (1/12)e^x + (3)e^−x for ln2 ≤ x ≤ ln4?

I can't seem to get the right answer. I got the derivative of the curve, plugged it into the formula, and still can't get it. Am I missing some trick?

Thanks!

2. ## Re: Arc Length of Curve!

hi

look at this link:Arc length - Wikipedia, the free encyclopedia

search the part called Finding arc lengths by integrating

3. ## Re: Arc Length of Curve!

I know how to do it. I've done these questions before. But I can't seem to get the answer with this one.

4. ## Re: Arc Length of Curve!

Originally Posted by bhaktir
What is the arc length of the part of the curve y= (1/12)e^x + (3)e^−x for ln2 ≤ x ≤ ln4?

I can't seem to get the right answer. I got the derivative of the curve, plugged it into the formula, and still can't get it. Am I missing some trick?

Thanks!
note ...

$\displaystyle y' = \frac{e^x}{12} - 3e^{-x}$

$\displaystyle (y')^2 = \frac{e^{2x}}{144} - \frac{1}{2} + 9e^{-2x}$

$\displaystyle 1 + (y')^2 = \frac{e^{2x}}{144} + \frac{1}{2} + 9e^{-2x} = \left(\frac{e^x}{12} + 3e^{-x}\right)^2$

ball is in your court ... finish it.