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Homework Help: Integral (9-4x^2)^1/2

  1. Jul 18, 2015 #1
    • Member warned about posting with no template
    Screen Shot 2015-07-18 at 10.54.39 PM.png Hey everyone, I'm currently studying for Calc 3 and came across this integral that his been racking my brain beyond insanity. I know the solution is easier than it is. I have looked online and come across substituting to have x=2sin(theta).

    I also came across a step where you substitute u for 2x leaving you with:

    integral of (25-u2)1/2

    I feel like there is a simpler way to solve it but I can't seem to see it

    Any help will greatly be appreciated.
  2. jcsd
  3. Jul 18, 2015 #2
    This problem begs to be solved by trig substitution. Try ##x=\frac{3}{2}\sinθ##, and then see if you can figure out why it works so well.

  4. Jul 18, 2015 #3
    Substitute x= (3/2)×sin(θ) .
  5. Jul 18, 2015 #4


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    It's not clear that making the substitution u = 2x into (9 - 4x2)1/2 leads to (25 - u2)1/2.

    Have you tried this yourself and worked out the algebra to confirm?

    In any event, dust off your trig identity knowledge. I'm not saying that the substitution x = 2 sin θ is correct here, but trig substitution is one way to go.
  6. Jul 18, 2015 #5
    Alright I posted some of the work but I'm having trouble with the dx and d(theta).

    Attached Files:

  7. Jul 18, 2015 #6
    You haven't substituted correctly for dx .
  8. Jul 18, 2015 #7
    Also you need to now change the limits of your integral .
  9. Jul 18, 2015 #8
    Forgot to change the limits but I think I correctly included dx as d(theta)

    Attached Files:

  10. Jul 18, 2015 #9
    You are supposed to substitute dx by (3/2)×cos(θ).dθ
  11. Jul 18, 2015 #10
    Sorry added the wrong pic

    Attached Files:

  12. Jul 18, 2015 #11
    So now just change your limits and you will get the answer .
  13. Jul 18, 2015 #12
    Alright great got it!!!! Thanks for the help everyone.
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