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

Integration by parts form

  1. Dec 4, 2014 #1
    I have a question why everyone says
    ∫uv' dx=uv-∫u'v dx
    why dont they replace v' with v and v with ∫vdx and say
    ∫uv dx=u∫vdx-∫(u'∫vdx) dx

    i think this form is alot simpler because you can just plug in and calculate, the other form forces you to think backwards and is unnecessarily complicated.
     
  2. jcsd
  3. Dec 4, 2014 #2

    Mark44

    Staff: Mentor

    Show us an example of how this would work, with say ##\int xe^xdx##.
     
  4. Dec 4, 2014 #3
    u=x
    v=e^x
    ∫(x*e^x)dx=x*∫e^xdx-∫e^xdx
    =xe^x-e^x+c

    right? its alot simpler than thinking backwards and doing the substitution i always have to right it down my way cause the other way is too complicated.

    edit: i just noticed that perhaps some people may be confused as to where the constant of integration goes
    ∫(x*e^x)dx=x*∫e^xdx-∫e^xdx
    ∫(x*e^x)dx=x*(e^x+c)-(e^x+c)
    this would be wrong but as long as you keep in mind that the constant cooresponds to a vertical translation you cant go wrong. so im guessing for the sake of mathematical rigor they use the other form?
     
    Last edited: Dec 4, 2014
  5. Dec 4, 2014 #4

    Mark44

    Staff: Mentor

    You checked it, didn't you?
    I think of it like this: ∫v du = uv - ∫u dv. That's not very complicated.
    Ignore it in your intermediate work. Just add it at the end.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Integration by parts form
  1. Integration by parts (Replies: 13)

  2. Integration by parts (Replies: 1)

  3. Integration by parts (Replies: 1)

  4. Integration by parts (Replies: 7)

  5. Integration By Parts (Replies: 2)

Loading...