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.
Stacey Warren - Expert brainly.com
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In a nutshell: I ended up with the right integral but if I plug in my boundaries (0 and 2pi) I get 0 as the lenght of the curve. So somehow the lenghts eat each other up?
So, how do I "use" the integral in the right way to get 8 as a lenght?
hmm to make the math work maybe you should split it into 2 integrals with limits (0,pi) and (pi,2pi)
This is very strange, wolfram does indeed give the answer as 8
yet whenever i try and evaluate the integral I get zero
just think 0 and 2pi are the same value when evaluated at cos(t) no wonder its zero, yet wolfram says otherwise.
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Changing the boundaries from before 0 to 2pi to 0 to pi and pi to 2pi did not help at all.
I only started learning about calculating the length of a curve so I have no clue what this is supposed to tell me. The Curce must clearly have some length.