1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integral (9-4x^2)^1/2

Tags:
  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.

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

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Integral (9-4x^2)^1/2
  1. Integrate sqrt(1+4x^2) (Replies: 4)

  2. Integrating (4x+1)^1/2 (Replies: 5)

Loading...