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Homework Help: Integration question

  1. Jan 22, 2005 #1
    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).
     
    Last edited: Jan 23, 2005
  2. jcsd
  3. Jan 23, 2005 #2

    Tide

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    Are you sure you copied the question correctly?
     
  4. Jan 23, 2005 #3
    does it seem right now?
     
  5. Jan 23, 2005 #4
    Shouldn't it be f² in the solution in stead of f" ???

    i mean the integrand is f * df/dt * dt right? so you have f * df as integrand

    marlon
     
  6. Jan 23, 2005 #5

    dextercioby

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    1.DO NOT DOUBLE POST!!!!!!!!!!!

    2.It's definitely
    [tex] f^{2}(t) [/tex]

    The hint is good.I guess u needed us to tell u that u didn't copy the exercise properly. :tongue2:

    Daniel.
     
  7. Jan 23, 2005 #6
    yes, you are right marlon, my bad all the way
     
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