1. ## Line Integrals

I'm having a difficult time understanding line integrals, here's the problem I'm working on, any help would be great, thanks in advance

Given the equation: xy = 18, set up an integral to find the length of path from x=a to x=b

2. Originally Posted by N736RA
I'm having a difficult time understanding line integrals, here's the problem I'm working on, any help would be great, thanks in advance

Given the equation: xy = 18, set up an integral to find the length of path from x=a to x=b
solving for y gives

$y=\frac{18}{x}$

$\int_{a}^{b}\sqrt{1+(y')^2}dx=\int_{a}^{b}\sqrt{1+ (\frac{-18}{x^2})^2}dx=\int_{a}^{b}\sqrt{\frac{x^4+324}{x^ 4}}dx$

I will let you work on the Integral

I hope this helps

3. thanks! My only question here is how did you get from 18/x to the radical formula? thanks again

4. Originally Posted by N736RA
thanks! My only question here is how did you get from 18/x to the radical formula? thanks again
You substitute $y' = \frac{dy}{dx}$ into the given formula $
\int_{a}^{b} \sqrt{1+(y')^2} \, dx$
. You are familiar with this arclength formula, right?

5. mr fantastic- ah I see now, I was actually not familiar with that formula, its a calc 2 online course, and the notes provided by the prof. are pretty difficult to decipher, now I've found the section though, thanks!