2.3. ARC LENGTH, PARAMETRIC CURVES 57 2.3. Arc Length, Parametric Curves 2.3.1. Parametric Curves. A parametric curve can be thought of as the trajectory of a ...
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...Arc length parametric curves a curve can be thought of as the trajectory point that moves trough plane with coor dinates x y f t g where and are functions parameter for each value we get example aparametric equation circle radius center is cost sint equations called given sometimes eliminate obtain anequivalent non same instance eliminated from by using trigonometric relation cos sin which yields find following para metric answer isolating it second plugging in rst i e parabola horizontal axis here describe how to nd smooth graph continuous function whose derivative also so does not have corner points if just straight line between two coordinates its found pythagorean theorem p l more generally approximate inscribing polygonal made up segments adding lengths assume b divide interval into n subintervals equal corresponding consecutive separated distance wehave ti on other hand mean some hence li total xp si converges integral z bp dt this formula expressed easier remem ber way bs dx dy ...