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UnkleRhaukusBest ResponseYou've already chosen the best response.2
in my book there is a question involving a term like this \[\int\limits_p^\infty F(p)\cdot\text dp \], but this is a confusing choice of notation because the variable of integration is one one of limits of integration
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
as far as i know the convention is to change to \[\int\limits_p^\infty F(p')\cdot\text dp'\] but i dont like this because it looks like the prime of p
 one year ago

ash2326Best ResponseYou've already chosen the best response.0
As we know that integration is independent of variable. You could use any variable of your choice. I'd go with the first one :)
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
\[\int\limits_p^\infty F(a)\cdot\text da\]
 one year ago

mukushlaBest ResponseYou've already chosen the best response.0
\[\int\limits_p^\infty F(x)\cdot\text dx\]
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
\[\int\limits\limits_p^\infty F(mukushla)\cdot\text d(mukushla)\]
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
the notation is still troubling me
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
well i kinda had to change the question so i could answer it
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
\[\begin{align*} \int\limits_p^\infty F(q)\cdot\text dq &=\int\limits_p^\infty\int\limits_0^\infty f(x)e^{qx}\cdot\text dx\cdot\text dq \\&=\int\limits_0^\infty f(x)\int\limits_p^\infty e^{qx}\cdot\text dq\cdot\text dx \\&=\int\limits_0^\infty f(x)\left.\frac{e^{qx}}{x}\right_p^\infty \cdot\text dx \\&=\int\limits_0^\infty \frac{f(x)}xe^{px}\cdot\text dx \\&=\mathcal L\left\{\frac {f(x) }x \right\} \end{align*}\]
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
do you understand why i am getting confused/
 one year ago

waterineyesBest ResponseYou've already chosen the best response.0
The things you are doing are going above my head, but I am not understanding why are you getting confused, where are you not feeling comfortable??
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
well the question in the book makes no sense
 one year ago

sasogeekBest ResponseYou've already chosen the best response.0
certainly this is confusing, but why not use usubstitution for F(p) ?
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
like this? \[\begin{align*} \int\limits_p^\infty F(p)\cdot\text dp\\ \text{let }u=p\\ \text du=\text dp\\ \\p=p\rightarrow u=u\\ p=\infty\rightarrow u=\infty\\ \\&=\int\limits_u^\infty F(u)\cdot\text du\\ \end{align*}\]
 one year ago

sasogeekBest ResponseYou've already chosen the best response.0
\(let \ u=F(p)\) \(\large \frac{du}{dp}=F'(p)\) \(\large dp =\frac{du}{F'(p)} \) \[\int\limits_{p}^{\infty}u \ \frac{du}{F'(p)}\]
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
im not sure why you'd do that?
 one year ago

sasogeekBest ResponseYou've already chosen the best response.0
well having the function variable being the same as one of the limits... i'm not quite sure how you'd go about solving it but thats the first thing that comes to my mind. besides, i'm not so good at calculus, but that's what i'd do. it may or may not be right, but it's worth a shot :/. I'm pretty certain this isn't calculus 1... right?
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
differential equations; laplace transforms
 one year ago

sasogeekBest ResponseYou've already chosen the best response.0
there we go, that's beyond me lol, but all things being equal, thats what i'd do. sorry i wasn't of much help lol :/ but i'll stick around to learn :)
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
but the problem im having is not the content of the question, i think i have answered that satisfactorily , my issus is the choice of notation used in the question
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
i dont think the question makes sense as written \[....=\int\limits_p^\infty F(p)\text dp\] it dosent make sense to have the variable as a limit of integration
 one year ago

sasogeekBest ResponseYou've already chosen the best response.0
you could ask satellite73 or amistre when they get online....
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
yeah, i looked at this earlier and dont have anything pertinent to add to it :/ srry
 one year ago
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