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Compute the average curvature of the curve

$\qquad r(t) = ⟨t \cos t,\, t \sin t⟩\ \mathrm{for}\ 0 ≤ t ≤ 2π$.

Use Mathematica to arrive at an exact value and its numerical approximation. Please include a printout of any Mathematica that you use in this problem.

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    $\begingroup$ Welcome to MSE. This looks like a homework problem. Have you attempted to solve it? Please post the code that you tried. $\endgroup$ – Rohit Namjoshi Nov 5 '19 at 20:44
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Since this is a simple homework problem, I don't think it would fair to just hand you the whole answer, but here are some hints.

To compute an exact expression for the mean curvature, use ArcCurvature andIntegrate.

When you have the exact expression, let us call it avgCrv, then you can get an approximate numerical value with

N[avgCrv]

0.561

You can use the the above value to check your work.

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