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Homework Help: Partial Fractions, Irreducible quadratic factors

  1. Oct 26, 2007 #1
    Arc Length, Irreducible quadratic factors

    i'm having a hard time seeing this method, and i have to use this method on one of the problems i'm doing to find it's Arc Length.

    [tex]L=\int_{\sqrt{2}}^{\sqrt{1+e^{2}}}\frac{v^{2}dv}{v^{2}-1}}[/tex]

    the book suggests to first divide then use a u-substitution. i know that when the power in the numerator is greater than the denominator, i can perform long-division, but i don't see how i can divide this.
     
    Last edited: Oct 26, 2007
  2. jcsd
  3. Oct 26, 2007 #2
    i dont know whether i am gettin u well, but you could do this inegral by doing this to the function under the integral sign

    v^2/(v^2-) =(v^2-1+1)/(v^2-1) = (1- 1/(v-1)(v+1) )

    then you could use partial fraction by letting

    1/(v-1)(v+1) = A/(v-1) + B /(v+1), and then finding the values of B and A. Pardone me if i misunderstood u.
     
  4. Oct 26, 2007 #3

    Gib Z

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    Homework Helper

    Well, like sutupidmath did, add one and then subtract one to the numerator. Then, instead of factoring the new denominator and partial fractions-ing, Try a hyperbolic substitution, I think you will find it quicker.
     
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