# Silly question...

by eljose
Tags: silly
 P: 501 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...
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,682 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.
 Emeritus Sci Advisor PF Gold P: 16,091 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)