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Homework Help: Why is this happening (trig subs)

  1. Dec 18, 2007 #1
    Dor the integral 1/x*sqrt(t^2 - 1)

    After i do the substitutions, it comes out to be sec(x)tan(x)/sec(x)tan(x), so evertything cancels out and the integral evaluated is just x (or theta), but what do I sub theta for when evaluating the integral?

    I know this is supposed to be arcsec, but I am not visualizing how I get to that point.

    Thank you.
  2. jcsd
  3. Dec 18, 2007 #2
    two variables ... which variable are you integrating with respects to?
  4. Dec 18, 2007 #3

    I guess I have to change the limits of integration.
  5. Dec 18, 2007 #4
  6. Dec 18, 2007 #5
    yes, letting x= sec[itex]\theta[/itex]

    If i let sqrt(2) = sec[itex]\theta[/itex] , I am looking for arcsec(sqrt(2)) , which is pi/ 4 since cos (pi/4) = 1/sqrt(2), so I would convert the limits. I gorgot that was required since we are mostly doing indefinite integrals.
  7. Dec 18, 2007 #6


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    Science Advisor

    No that wasn't the question- your original integral involves both x and t. Was that an typo? Did you mean dx/(x*sqrt(x^2-1)) or dt/(t*sqrt(t^2-1))?
  8. Dec 18, 2007 #7
    was typo.
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