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Mathematics, 28.10.2019 21:31 chaseashley24

The total curvature of the portion of a smooth curve that runs from sequalss 0 to s 1 greater than s 0 can be found by integrating kappa from s 0 to s1. if the curve has some other parameter, say t, then the total curvature is upper k equals integral from s 0 to s 1 kappa ds equals integral from t 0 to t 1 kappa startfraction ds over dt endfraction dt equals integral from t 0 to t 1 kappa startabsolutevalue bold v endabsolutevalue dt , where t0 and t1 correspond to s 0 and s1. a. find the total curvature of the portion of the helix bold r (t )equals (3 bold font size decreased by 1 cos font size decreased by 1 t )bold i plus (3 bold font size decreased by 1 sin font size decreased by 1 t )bold j plus t bold k, 0 less than or equals t less than or equals 4 pi . b. find the total curvature of the parabola yequals4 x squared, minusinfinityless thanxless thaninfinity.

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