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Thread: Please help me wih this calculus equation

  1. May 23rd 2012, 10:25 AM #1
    Adgh
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    Please help me wih this calculus equation

    Sketch the curve and find its arc length
    r(t) = (cos π t, sin π t, cos 4 π t), 0 ≤ t ≤ 2
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  2. May 23rd 2012, 02:48 PM #2
    HallsofIvy
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    Re: Please help me wih this calculus equation

    Quote Originally Posted by Adgh View Post
    Sketch the curve and find its arc length
    r(t) = (cos π t, sin π t, cos 4 π t), 0 ≤ t ≤ 2
    It might help to note that, for all t, x^2+ y^2= cos^2(\pi t)+sin^2(\pi t)= 1 so the projection into the xy- plane is a circle. How does z vary?

    The arclength is, of course \int_0^2\sqrt{\left(\frac{d cos(\pi t)}{dt}\right)^2+ \left(\frac{d sin(\pi t)}{dt}\right)^2+ \left(\frac{d cos(4\pi t)}{dt}\right)^2} dt.

    Can you do that?
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