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Required to prove that ∫f(x)dx[b, a] =∫f(x−c)dx [b+c, a+c]

  1. Apr 1, 2012 #1
    1. The problem statement, all variables and given/known data
    required to prove that
    ∫()[, ] =∫(−) [+, +]

    where f is a real valued function integrable over the interval [a, b]

    2. Relevant equations

    ∫() [, ]=()−()

    3. The attempt at a solution


    ∫() [b, a]=()−()

    ∫(−) [+, +]=(+−)−(+−)=()−()
    ∴∫()[, ] =∫(−) [+, +]

    right i placed the interval in the [] brackets


    is this correct?
     
  2. jcsd
  3. Apr 1, 2012 #2

    Dick

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    Re: required to prove that ∫()[, ] =∫(−) [+, +]

    You just assumed that the antiderivative of f(x-c) is F(x-c). Why is that true?
     
  4. Apr 1, 2012 #3
    Re: required to prove that ∫()[, ] =∫(−) [+, +]

    i believe it was given in a lecture i had so i assumed is that a wrong assumption?
     
  5. Apr 1, 2012 #4

    Dick

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    Re: required to prove that ∫()[, ] =∫(−) [+, +]

    It's not a wrong assumption. It just needs to be proved. If F'(x)=f(x), why is F'(x-c)=f(x-c)? It's easy, but you should say why. Use the chain rule. In other language, they may expect you to prove this using the substitution u=x-c. Why is dx=du?
     
    Last edited: Apr 1, 2012
  6. Apr 2, 2012 #5

    Borek

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    You are probably not aware, but the way you posted makes your post unreadable to at least XP Windows users using Chrome, IE & Opera, attachment shows what they see. It looks little bit better under Vista, but is still barely readable.

    I have corrected thread subject.
     

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