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!

A question of taking integral

  1. Sep 17, 2011 #1
    1. The problem statement, all variables and given/known data

    Solve the integral.

    2. Relevant equations

    Integral: (x^m)*(1-x)^k where m is a nonnegative integer and k > -1

    3. The attempt at a solution

    I've tried to take this integral by using integral by parts, but I couldn't take it. Can anyone tell me how to take this integral? I really appreciate that.
     
  2. jcsd
  3. Sep 18, 2011 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    If it's an indefinite integral then that's an incomplete beta function. You can do a lot of things with it, but you can't write a simple elementary form for it. What do they really want you to do?
     
  4. Sep 18, 2011 #3
    Sorry. the integral is actually 1 to 0. This question is actually induction.

    Integral(1-0): (x^m)*(1-x)^k=n!/(k+1)(k+2).....(K+m+1) where m is a nonnegative integer and k > -1

    So, I thought that if I take integral from the right side, I can prove it. But it does not seem the case...
     
  5. Sep 18, 2011 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Then start working on the integration by parts idea. Call your integral I(m,k). Work out m=0. For practice try doing small values of m (m=1, m=2, m=3) until you see what's going on. Then try to express I(m+1,k) in terms of I(m,k) and apply induction.
     
    Last edited: Sep 18, 2011
  6. Sep 18, 2011 #5
    actually, I think I made it. Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: A question of taking integral
Loading...