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Integration of a Square Root including constants

  1. Aug 10, 2011 #1
    1234
     
    Last edited: Aug 10, 2011
  2. jcsd
  3. Aug 10, 2011 #2

    Char. Limit

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    Have you tried trig substitution? let x = 3sin(s) and then substitute in... you should get an expression that you can integrate, after a few trig tricks of course.
     
  4. Aug 10, 2011 #3
    1234
     
    Last edited: Aug 10, 2011
  5. Aug 10, 2011 #4

    Char. Limit

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    It's just an intuitive solution I look at when I see a square root like that. If you substitute it in, you get sqrt(1 - (3 sin2(s))/9), or sqrt(1 - sin2(s)). This, as we know, is equal to cos(s), which is easy to integrate. Then we just need to handle the dx...

    But I think once you have x = 3 sin(s), dx should be easy to find. :)
     
  6. Aug 10, 2011 #5
    1234
     
    Last edited: Aug 10, 2011
  7. Aug 10, 2011 #6

    Char. Limit

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    You have a mistake at two places. The sin^2(s) should be (3 sin(s))^2 and the 3 needs to be a 9. Other than that, you're so-far good. After substituting, you should get an easy 3+2cos(s), which of course needs to be multiplied by dx. So while you're doing that, it might be a good idea to get dx in terms of ds.
     
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