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

## Homework Statement

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

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

∫() [, ]=()−()

## The Attempt at a Solution

∫() [b, a]=()−()

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

right i placed the interval in the [] brackets

is this correct?

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Dick
Homework Helper

You just assumed that the antiderivative of f(x-c) is F(x-c). Why is that true?

i believe it was given in a lecture i had so i assumed is that a wrong assumption?

Dick
Homework Helper

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:
Borek
Mentor
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.