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Math Help - Question about line integral

  1. #1
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    Question about line integral

    let \kappa denote the curvature of a closed spacecurve \alpha. Find \oint_{\alpha} \frac{1}{\kappa} \ d\kappa

    Looking at this, I would imagine that this would either be 0 since \alpha is closed or T, the tangent Vector, but I'm not to sure on how to achieve the desired result.

    My other idea would have been to write it down as follows:

    \oint_{\alpha} \frac{\|\alpha'\|^3}{\|\alpha' \times \alpha''\|} \cdot \|\alpha'\| \ dt

    But these attempts don't seem to lead to anything.
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  2. #2
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    \oint_{\alpha} \frac{1}{\kappa} \ d\kappa = \oint_{\alpha} d \ln | \kappa | = 0
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