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Homework Help: Curve integral

  1. Nov 1, 2005 #1
    How can I find average distance from the origin point x=y=0 to
    the points of the curve using curve integral.

    Curve given by

    x=cos(2t), y=3sin(2t), t at [0,pi]

    I looked in books I have but there is no info on this.
     
  2. jcsd
  3. Nov 1, 2005 #2
    Find an equation that gives the distance at any value of t. Then integrate it and divide by the interval (def. of average value).
     
  4. Nov 1, 2005 #3
    I need to find it using curve integral
     
  5. Nov 1, 2005 #4
    Ok. I integrated equation that give the distance.

    I got

    Integral ((cos^2(2t)+6sin^2(2t))^0.5)*dt integral from 0 to pi

    Did I get it right?
     
  6. Nov 1, 2005 #5

    NateTG

    User Avatar
    Science Advisor
    Homework Helper

    Close. You need to be more careful with your derivatives and algebra.
     
  7. Nov 1, 2005 #6
    [tex]3^2\neq 6[/tex]

    For this case:

    [tex]\text{Average}=\frac{1}{\pi}\int_{0}^{\pi}f\left(x\right)\,dx[/tex]

    Now it's up to you to find f(x).
     
    Last edited: Nov 1, 2005
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