An arc length integral in 3D
The groovy trefoil pic on our class web page is parameterized by
x(t) = \sin(3t) \\
y(t) = \sin(t) + 2\sin(2t) \\
z(t) = \cos(t) - 2\cos(2t)
over the interval $[0,2\pi]$.
- Type out an integral representing the arc length of the trefoil knot and
- Find a numerical estimate of your integral.
Of course, you can try to generate a 3D image of the trefoil knot on math3d.org if you like, but it might not look quite as groovy as the one on our web page!