Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integration of the binomial theorem

  1. Dec 8, 2008 #1
    is it possible to integrate the binomial theorem??
     
  2. jcsd
  3. Dec 8, 2008 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hiho hmmmmm! Welcome to PF! :smile:
    Yes, and that should give you an equation relating nCk and n-1Ck-1

    what is it? :smile:
     
  4. Dec 8, 2008 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What do you mean by "integrating a theorem", integrating both sides of the equation involved? If so, yes, tiny-tim is correct.
     
  5. Dec 10, 2008 #4
    ok so what would happen if you integrated both sides of it then.
     
  6. Dec 10, 2008 #5

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    uh-uh … you tell us! :smile:
     
  7. Dec 10, 2008 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    1) Write down the formula for "the binomial theorem."

    2) Integrate each side separately. That shouldn't be difficult, they both involve just the "power rule", that the integral of xn is (1/n+1)xn+1+ a constant.

    What do you get?
     
  8. Dec 11, 2008 #7
    yes this is the part i dont understand how you would integrate (a^x+B)^y once expanded not in the braket.
     
  9. Dec 11, 2008 #8

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    "(a^x+ B)^y is NOT a binomial form. Do you mean (Ax+ B)^y where A, B, and y are constants? If so, do not expand it. Make the substitution u= Ax+ B so that du= Adx and dx= (1/A)du.
     
  10. Dec 12, 2008 #9
    i mean the integral of (a^x+b)^y da where x b and y are constants sorry for my sloppy notation
     
  11. Dec 12, 2008 #10

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Good! So do what we have been encouraging you do to all along! Write out (a^x+ b)^y in terms of the binomial expansion and integrate, term by term.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Integration of the binomial theorem
  1. Binomial Theorem? (Replies: 3)

Loading...