Paper 3, Section I, C

Vector Calculus | Part IA, 2013

The curve CC is given by

r(t)=(2et,etsint,etcost),<t<\mathbf{r}(t)=\left(\sqrt{2} e^{t},-e^{t} \sin t, e^{t} \cos t\right), \quad-\infty<t<\infty

(i) Compute the arc length of CC between the points with t=0t=0 and t=1t=1.

(ii) Derive an expression for the curvature of CC as a function of arc length ss measured from the point with t=0t=0.

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