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Calculus with Parametric Curves

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Find the exact length of the curve
x = 3*cos(t) - cos(3*t), y = 3*sin(t) - sin(3*t)

The curve is plotted in the attachment. How would I integrate the derivatives to get the length of the curve?

I think I have to integrate this in several steps, accounting first for the parts below the x-axis, and then for the curve above the x-axis. To do that, I have to find out for what values of t result in negative values for y.

See the attached file.

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The solution calculates a calculus with parametric curves.

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