I want to find the length of a curve which is given by the equation: r=(t-sint,1-cost, 2).
To calculate the length I first calculate the first derivative of r which is v=(1-cost, sint, 0).
Than I went on to integrate the absolulte value of v.
This gave me the integral of the squareroot of (2-2cost). Than I ended up with -2*squareroot of (2+2cost). Which is the same as Wolfram Alpha got.
However, if I want to integrate this curve from 0 to 2pi than I end up with 0, but it should be 8. If I plug in 0 and 2pi I get -4-(-4) which is 0, but the curve can not have a lenght of 0.

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hmm to make the math work maybe you should split it into 2 integrals with limits (0,pi) and (pi,2pi)

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