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Math Help - length of parametric curve

  1. #1
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    length of parametric curve

    consider the parametric equation

    x=10(cos∅+∅sin∅)
    y=10(sin∅-∅cos∅)

    what is the length of the curve for ∅=0 to ∅=1/6∏?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by waite3 View Post
    consider the parametric equation

    x=10(cos∅+∅sin∅)
    y=10(sin∅-∅cos∅)

    what is the length of the curve for ∅=0 to ∅=1/6∏?
    do you have the right integral?

    the arc length is given by: L = \int_0^{1/6 \pi} \sqrt{\left( \frac {dx}{d \theta} \right)^2 + \left( \frac {dy}{d \theta} \right)^2 }~d \theta
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  3. #3
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    ya i have that but everytime i take the derivative of x and y then plug them into the equation i come out with the wrong answer. what do you come out with for an answer. thanks for your help
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by waite3 View Post
    ya i have that but everytime i take the derivative of x and y then plug them into the equation i come out with the wrong answer. what do you come out with for an answer. thanks for your help
    for the integral, i got 5 \theta^2 + C, now just evaluate that between the given limits
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  5. #5
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    i come out with 0.239245 and its not right.
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    Quote Originally Posted by waite3 View Post
    i come out with 0.239245 and its not right.
    of course that is wrong. that is not what you get when you evaluate.

    you have 5 \theta^2 \big|_0^{1 / 6 \pi} = 5 \left( \frac 1{6 \pi} \right)^2 {\color{red}\ne} ~0.239245
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