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Math Help - Integration along a path

  1. #1
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    Integration along a path



    how do i approach this question please?



    I dont understand the substitution from ds to dx.



    thanks.
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  2. #2
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    Re: Integration along a path

    Hey BabyMilo.

    Have you tried a contour integral by parametrizing the curve over some interval?

    Standard parametrization for y = ax^2 + bx + c is to use the parameterization x = t and y = at^2 + bt + c.

    Have you covered contour integration with parameterizations of a parabola?
    Thanks from topsquark
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  3. #3
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    Re: Integration along a path

    The practical way of looking at it is

    ds^{2}=dx^{2}+dy^{2}=\left\{1+\left(\frac{dy}{dx} \right)^{2} \right\}dx^{2},
    so
    ds=\sqrt{1+\left(\frac{dy}{dx}\right)^{2}} \quad dx
    Thanks from BabyMilo and topsquark
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  4. #4
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    Re: Integration along a path

    Quote Originally Posted by chiro View Post
    Hey BabyMilo.

    Have you tried a contour integral by parametrizing the curve over some interval?

    Standard parametrization for y = ax^2 + bx + c is to use the parameterization x = t and y = at^2 + bt + c.

    Have you covered contour integration with parameterizations of a parabola?
    No i have not covered contour integration with parameterizations of a parabola.

    But thanks.
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