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Guessing the Value of an Integral

  1. Mar 2, 2016 #1

    Drakkith

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    Staff: Mentor

    1. The problem statement, all variables and given/known data
    Guess the value of the following integral when n is an arbitrary positive integer.
    Evaluated from 0 to infinity: ∫30xne-x dx

    2. Relevant equations


    3. The attempt at a solution

    I've evaluated the integral for values of n from 0 to 3:

    n=0: 30
    n=1: 30
    n=2: 60
    n=3: 180

    The pattern appears to be that each value is n times larger than the previous value, but I have no idea how to express that mathematically.
     
  2. jcsd
  3. Mar 2, 2016 #2

    Charles Link

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    Homework Helper

    An integration by parts gives F(n)=n*F(n-1) where F(n) is the value of the integral for the value n. Meanwhile, the number 30 is just a constant. The value of F(n) is thereby F(n)=30* (n !) where n !=n(n-1)(n-2)...2*1
     
  4. Mar 2, 2016 #3
    Hi Drakkith:

    I think the following will be helpful.

    In particular, take a look at the introduction and also the section
    The Gamma and Pi functions.​

    Regards,
    Buzz
     
  5. Mar 2, 2016 #4

    Drakkith

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    Staff: Mentor

    30n! turned out to work. Thanks!
     
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