Web Reference: Apr 25, 2015 · This parameterization looks qualitatively different from the trigonometric parameterization $\gamma (t)$ above, but they are related by a clever and important change of variable related to Pythagorean triples and which proves to be extremely helpful in evaluating certain integrals. Consider the parameterization of the unit circle given by x = cos (ln (t)), y = sin (ln (t)) for t in (0,infinite). Describe in words and sketch how the circle is traced out, and use this to answer the following questions. Parameterization is necessary to capture what your curve actually is but the particular parameterization used doesn't matter. If you setup the same line integral with two different parameterizations, those integrals will just differ by a u-substitution.
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