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Silly question...

by eljose
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eljose
#1
Sep30-05, 09:34 AM
P: 501
are the integrals:

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

[tex]\int_a^{b}dnf(t,n)r(n)+\int_a^{b}dkf(t,k)g(k) [/tex] 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...
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HallsofIvy
#2
Sep30-05, 09:51 AM
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PF Gold
P: 39,563
You seem to have lost a couple of right parentheses.
If you meant:
[tex]\int_a^{b}dnf(t,n)[r(n)+g(n)] [/tex]


Yes, they are exactly the same.
Hurkyl
#3
Sep30-05, 09:41 PM
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A technicality:

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


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