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Math Help - length of curve

  1. #1
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    length of curve

    find the length of the curve r(t) = tcost i + tsint j + sqrt(2)t k ,
    0 <= t <= 1

    help with this one please.
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  2. #2
    Senior Member
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    Quote Originally Posted by rcmango View Post
    find the length of the curve r(t) = tcost i + tsint j + sqrt(2)t k ,
    0 <= t <= 1

    help with this one please.
    r(t) = <t*cos(t), t*sin(t), sqrt(2)*t>

    r'(t) = <cos(t) - t*sin(t), t*cos(t) + sin(t), sqrt(2)>

    arclength = int(sqrt[(cos(t) - t*sin(t))^2 + (t*cos(t) + sin(t))^2 + 2]dt)

    I'll let you do the simplifying, but it turns out to simplify to:

    int(sqrt(t^2 + 3)dt) = (3*ln(sqrt(t^2 + 3) + t))/2 + (t*sqrt(t^2 + 3))/2

    From t = 0...1, we have:

    3*ln(3)/4 + 1 ~ 1.824
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