Are these two integrals the same?

[eljose]

silly question...

are the integrals:

$$\int_a^{b}dnf(t,n)[r(n+g(n]$$ and

$$\int_a^{b}dnf(t,n)r(n)+\int_a^{b}dkf(t,k)g(k)$$ the same?..i know that n and k are dummy variable so we can always make the change of variable k=n or n=k inside one of the two integral...

 

[HallsofIvy]

You seem to have lost a couple of right parentheses.
If you meant:
$$\int_a^{b}dnf(t,n)[r(n)+g(n)]$$


Yes, they are exactly the same.

 

[Hurkyl]

A technicality:

$\int f + g = \int f + \int g$ provided the two integrals on the right hand side exist. (Knowing the left hand side exists is not enough)