I'm wondering if this could be used to calculate the value of a contour integral directly. If a function has an antiderivative on the entire complex plane, this implies the field is conservative so we should always get the same value no matter which path taken. Shouldn't this also mean integrals could just be computed by the fundamental theorem of calculus as(adsbygoogle = window.adsbygoogle || []).push({});

##\int_\gamma f(z)dz = F(z)\bigg|_{z_1}^{z_2}##

where the curve is from ##z=z_1## to ##z=z_2##?

Yet I haven't actually seen a single example of this being done, every integral is computed by parametrization of the contour integral. Just doing a few examples It seems to work but doesn't this always work?

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# Antiderivative and contour integration

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