Arc Length of a Trefoil Knot

Choose parameters for your trefoil knot:

a=5;
b=2;
r[t_]={(a+b*Cos[3t])*Cos[2t],(a+b*Cos[3t])*Sin[2t],b*Sin[3t]}

Calculate the velocity vector:

r'[t]

Calculate the speed (and simplify):

Simplify[Sqrt[r'[t].r'[t]]]

Calculate the length by (numerically) integrating the speed:

NIntegrate[Simplify[Sqrt[r'[t].r'[t]]],{t,0,2Pi}]