An arc length integral in 3D

edited February 11 in Problems

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

  • edited February 13

    %%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

    mark
  • @fritz

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

    I wonder why Math3d would be blocked?!

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