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Circumference of a circle in parametrics

  1. Feb 10, 2010 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    length of curve square root (1+(dx/dy)^2)dy or square root ((dx/dt)^2 + (dy/dt)^2) dt

    3. The attempt at a solution[/b

    I isolated y and got y= square root (1-x^2)

    finding dy/dx = -x/square root (1-x^2)
    i plugged that into the formula but i did not get the correct answer.

    im aware that if i do integral of square root (1+ (dy/dx)^2 ) i have to do imporper integral as i get undefined for denominator at x=-1,1 so what should i do
    we all know that answer should be 2pi
  2. jcsd
  3. Feb 10, 2010 #2


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    Ignore the 'undefined' issue. Just do a trig substitution to solve the integral. Once you've done the trig substitution you won't see the singularity. BTW you'll get pi, not 2*pi. Your parametrization only covers half the circle.
  4. Feb 10, 2010 #3
    I know, i can get the answer by defining the circle in trig.

    But, shouldn't i be able to do it in conventional way and by paramatrization as well?
    i just need to take care of the x values and t values where the function gets undefined.
    My teacher wants me to do it in these two ways.
  5. Feb 10, 2010 #4


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    Even to do it in the x-y way you need to integrate 1/sqrt(1-x^2) from -1 to 1, right? Even if you haven't parametrized it as a trig function you still need to do a trig substitution to solve that integral. That's what I'm talking about.
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