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Integration problem

  1. Oct 24, 2007 #1
    1. The problem statement, all variables and given/known data

    Determine [tex]\int[/tex]4dy/(1+9y[tex]^{2}[/tex]) With limits of 2,0.

    2. Relevant equations

    3. The attempt at a solution

    Have attempted ingtegration by substitution but have had no luck solving this problem. A maths tutor who went over it very quickly established there was a tan in the answer, i have not integrated anything like this before so don't really know where to start.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 24, 2007 #2
    do you know what the derivative of arctan is?
  4. Oct 24, 2007 #3
    maybe this looks a little more familiar

    Last edited: Oct 24, 2007
  5. Oct 24, 2007 #4
    I have just looked up the definition, can't quite see how it will fit
  6. Oct 24, 2007 #5

    [tex]\mbox{Let u=3y}[/tex]

    does it look a little more familiar now?
  7. Oct 24, 2007 #6
    I ended up with


    Am i close?
  8. Oct 24, 2007 #7
    no, example

  9. Oct 24, 2007 #8
    Hmm i can't seem to get it, when i integrate i get

  10. Oct 24, 2007 #9
    Ignore that last post, is

    [tex]\frac{4}{3}tan^{-1}(6)[/tex] correct?
  11. Oct 24, 2007 #10
    do you notice the pattern with my problem?

    the angle is [tex]3y^{2}[/tex]

    where did my angle and derivative end up when i differentiated?
  12. Oct 24, 2007 #11
    you're constants are correct but you're angle is wrong. if i took the derivative of your problem it would end up being 0 b/c you're basically saying it's a constant.

  13. Oct 24, 2007 #12
    The 6 is just the value of the limits substituted in to get a final answer, or is not that what the substituted value would be?
  14. Oct 24, 2007 #13
    yes that is correct, i did not realize you were already plugging your limits in and evaluating. sorry, miscommunication.
  15. Oct 24, 2007 #14
    no problem, thank you very much for your assistance :)
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