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Math Help - Line Integrals

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by N736RA View Post
    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
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  3. #3
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    thanks! My only question here is how did you get from 18/x to the radical formula? thanks again
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  4. #4
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    Quote Originally Posted by N736RA View Post
    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 <br />
\int_{a}^{b} \sqrt{1+(y')^2} \, dx. You are familiar with this arclength formula, right?
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  5. #5
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    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!
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