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!

Basic Integration Techniques

  1. Mar 14, 2013 #1
    1. The problem statement, all variables and given/known data
    I am reviewing some basic integration techniques. how would i evaluate this?


    2. Relevant equations
    [itex]\displaystyle\int {\frac{1}{\sqrt{8x-x^2}} dx}[/itex]


    3. The attempt at a solution
    i've tried multiplying by

    [itex]\frac{\sqrt{8x-x^2}}{\sqrt{8x-x^2}}[/itex] but that isn't getting me anywhere.

    should i use something like completing the square?
     
  2. jcsd
  3. Mar 14, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Completing the square is a good way to begin. Afterwards, a clever substitution can help.
     
  4. Mar 14, 2013 #3
    okay. im stuck with the subtracted term.

    [itex]\frac{1}{-\sqrt{(x^2 - 8x + 16) - 16}}[/itex]

    [itex]\frac{1}{-\sqrt{(x-4)^2 - 16}}[/itex]
     
  5. Mar 14, 2013 #4
    i don't think completing the square works here.
     
  6. Mar 14, 2013 #5

    eumyang

    User Avatar
    Homework Helper

    Looks like you pulled a negative outside of the square root. You can't do that!!!! Try again.
     
  7. Mar 14, 2013 #6
    Once you've fixed up the negative, try the substitution u=(x-4) and then consider what the derivatives of the inverse trigonometric functions look like.
     
  8. Mar 14, 2013 #7
    great. thanks phosgene.

    so we are looking at:

    answer:
    [itex]arcsin(\frac{x-4}{4}) + c[/itex]
     
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: Basic Integration Techniques
  1. Integration techniques (Replies: 6)

  2. Integration techniques (Replies: 5)

  3. Integration techniques (Replies: 4)

  4. Integration techniques (Replies: 1)

Loading...