Sigma under an integral: int x sigma (n(n+1))/2

[jivid]

Hey there,
I wanted to know whether a summation under an integral such as this:

. . . . .\(\displaystyle \displaystyle \int\, x\, \)\(\displaystyle \displaystyle \sum\, \dfrac{n\, (n\, +\, 1)}{2}\)

...would come out of the integral unaffected or not, as if it's just a coefficient.
thanks

 

[Deleted member 4993]

Hey there,
I wanted to know whether a summation under an integral such as this

would come out of the integral unaffected or not, as if it's just a coefficient.
thanks

Are you integrating w.r.t.x or integrating w.r.t n?

 

[jivid]

got it already

Are you integrating w.r.t.x or integrating w.r.t n?

Hey Subhotosh Khan,
you're right. I was neglecting this point. it it's w.r.t.x, then the summation can come out unaffected; if it's w.r.t.n, then it would be different.
your question already answered my question.
who's to say "don't answer question with question?":lol::lol::lol:
Thank you.

 

[HallsofIvy]

Just to clarify, since others may still be wondering, \(\displaystyle \sum\frac{n(n+1)}{2}\) is a constant and can be taken out of the integral.