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Integration question

  1. Jan 23, 2005 #1
    I'm having major trouble with this question, can anyone assist me on this?

    Let f be a function such that f' is continuous on [a,b]. Show that

    [tex]\int_a^{b}[/tex] f(t)f’(t) dt = 1/2 [f''(b) - f''(a)]

    Hint: Calculate the derivative of F(x) = f''(x).
     
  2. jcsd
  3. Jan 23, 2005 #2

    Zurtex

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    Don't double post please
     
  4. Jan 23, 2005 #3
    sorry, i thought a different forum would make a difference, since no one has an answer to my question yet.
     
  5. Jan 23, 2005 #4

    Zurtex

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    Have you not read your other thread? People have been quite helpful.
     
  6. Jan 23, 2005 #5

    shmoe

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    Hi, are you sure those are second derivatives on the right hand side and not squares? Something like [tex]1/2(f(b)^2-f(a)^2)[/tex] instead?
     
  7. Jan 23, 2005 #6
    i'm not sure if they are squares becoz the question reads f^2(b) - f^2(a)..so i thought they were second derivative..
     
  8. Jan 23, 2005 #7

    Zurtex

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    That is squares and I am sure about that because it is the answer. When your talking about the nth derivative you either use roman numerals or put the number in brackets.
     
  9. Jan 23, 2005 #8
    Couldn't one simply integrate by parts to get the answer?
     
  10. Jan 24, 2005 #9
    Could you please explain how you come to that answer, I am having trouble seeing it.

    Thanks.
     
  11. Jan 24, 2005 #10

    shmoe

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    Just use the hint applied to [tex]F(x)=(f(x))^2[/tex]. Find the derivative of F(x) using the chain rule...


    DeadWolfe-yes integration by parts will work fine.
     
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