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

  • Thread starter jodecy
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  • #1
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Homework Statement


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

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

Homework Equations



∫() [, ]=()−()

The Attempt at a Solution




∫() [b, a]=()−()

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

right i placed the interval in the [] brackets


is this correct?
 

Answers and Replies

  • #2
Dick
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You just assumed that the antiderivative of f(x-c) is F(x-c). Why is that true?
 
  • #3
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i believe it was given in a lecture i had so i assumed is that a wrong assumption?
 
  • #4
Dick
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i believe it was given in a lecture i had so i assumed is that a wrong assumption?
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:
  • #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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