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Math Help - calculus, find length of curve

  1. #1
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    calculus, find length of curve

    Find the arc length of the curve
    y = - ln (cosx) for 0 <=x<=pi/4
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by harry View Post
    Find the arc length of the curve
    y = - ln (cosx) for 0 <=x<=pi/4
    The arc length is:

    s = integral(x=0 to pi/4) sqrt[1+(y'(x))^2] dx

    which in this case is:

    s = integral(x=0 to pi/4) sqrt[1+tan^2(x)] dx

    ...= integral(x=0 to pi/4) 1/cos(x) dx

    ...= ln[tan(pi/4+pi/8)] - ln[tan(pi/4)]

    ...= ln[tan(3 pi/8) / tan(pi/4)] ~= 0.8814

    RonL
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