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Thread: Arc Length of Sine Curve via Integration: square root of sin^2(x/1300) + 1

  1. #1

    Arc Length of Sine Curve via Integration: square root of sin^2(x/1300) + 1

    Hey,

    So I'm trying to find the arc length of a sine curve.

    I need to find the integral of the square root of sin^2(x/1300) + 1

    The square root is what screwed it up, cos I don't know how I can go about integrating a trig function with radical.

    How can I go about doing this?

    Thanks you very much!

  2. #2
    Elite Member
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    Quote Originally Posted by AbhiKap55 View Post
    Hey,

    So I'm trying to find the arc length of a sine curve.

    I need to find the integral of the square root of sin^2(x/1300) + 1

    The square root is what screwed it up, cos I don't know how I can go about integrating a trig function with radical.

    How can I go about doing this?

    Thanks you very much!
    The answer will be in elliptic functions. There is no closed-form solution.
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
    Quote Originally Posted by Subhotosh Khan View Post
    The answer will be in elliptic functions. There is no closed-form solution.

    Thanks for your reply. Can you please elaborate on how I can find the integral of this function if it is an elliptic function.

  4. #4
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    You use a "table of elliptic functions" to write the answer. Again, there is no "closed form solution".
    https://en.wikipedia.org/wiki/Elliptic_integral
    http://mathworld.wolfram.com/EllipticIntegral.html

  5. #5
    Quote Originally Posted by HallsofIvy View Post
    You use a "table of elliptic functions" to write the answer. Again, there is no "closed form solution".
    https://en.wikipedia.org/wiki/Elliptic_integral
    http://mathworld.wolfram.com/EllipticIntegral.html
    Several functions do not have an elementary antiderivative. Would the square root of the hyperbolic cosh function be one such function?
    Last edited by AbhiKap55; 11-28-2016 at 10:22 AM.

  6. #6
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    Quote Originally Posted by AbhiKap55 View Post
    Several functions do not have an elementary antiderivative. Would a hyperbolic cosh function be one such function?
    No

    d/dx sinh(x) = cosh(x)
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  7. #7
    Quote Originally Posted by Subhotosh Khan View Post
    No

    d/dx sinh(x) = cosh(x)
    My Apologies, Mr. Khan. I was referring to a function f(x) that is equal to the square root of the hyperbolic function cosh.

    Would f(x) be un-integratable?

  8. #8
    Quote Originally Posted by Subhotosh Khan View Post
    No

    d/dx sinh(x) = cosh(x)
    My Apologies, Mr. Khan. I actually meant to say if f(x) is a function equal to the square root of cosh(x)

    Would f(x) be un-integratable? Is there a way I can approximate the value?

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