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Using integral to find length of curve

  1. Mar 24, 2010 #1
    1. The problem statement, all variables and given/known data
    Ok, the problem is there are two curves and I need to find out which is shorter. I can't find the first one so I'll just post that. The other should be easy after I learn how to get this one.

    2. Relevant equations
    The first curve is:

    3. The attempt at a solution

    I used the formula EQ2.jpg and worked it down to EQ3.jpg .

    I've also seen some similar problems to this where people recommended trig substitutions. I tried substituting tan u in which gave me sec^2 u under the radical. If I go that route, I don't know the integral of sec or how you could carry on. The other way I thought you could do this was to just simplify (from the last picture I posted) and try to integrate that... but that would be rough. Any tips?
  2. jcsd
  3. Mar 24, 2010 #2


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    The integral of sec(x) is usually done with the trick of multiplying the numerator and denominator by (sec(x) + tan(x)) followed by a u-substitution. Try it.
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