Consider the spiral curves given parametrically by x(t) sin t tr where r > 0. 5.a Using that x' (t) = y(t) = t cost r sin t cos t tr and y' (t) " = t> 3 t sint + r cos t tr+1 tr+1 set up and simplify an (improper) integral that computes the arclength of these spirals. The integral will depend on r. 5.b For which r > 0 does this spiral have finite length? 5.c Compute the length of the spiral when r = 3.

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