# An arc length integral in 3D

The groovy trefoil pic on our class web page is parameterized by

$$

\begin{array}{l}

x(t) = \sin(3t) \\

y(t) = \sin(t) + 2\sin(2t) \\

z(t) = \cos(t) - 2\cos(2t)

\end{array}

$$

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!

## Comments

%%int_0^(2pi)sqrt(9cos(3t)^2+(cos(t)+4cos(2t))^2+(4sin(2t)-sin(t))^2)dt%%

%%~~28.83%%

Math3d is blocked at work, so I'll just refer to the webpage lol

@fritz

I wonder why Math3d would be blocked?!