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UnkleRhaukus Group TitleBest 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
 2 years ago

UnkleRhaukus Group TitleBest 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
 2 years ago

ash2326 Group TitleBest 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 :)
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
\[\int\limits_p^\infty F(a)\cdot\text da\]
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.0
\[\int\limits_p^\infty F(x)\cdot\text dx\]
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
\[\int\limits\limits_p^\infty F(mukushla)\cdot\text d(mukushla)\]
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
the notation is still troubling me
 2 years ago

waterineyes Group TitleBest ResponseYou've already chosen the best response.0
Where???
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
well i kinda had to change the question so i could answer it
 2 years ago

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

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
do you understand why i am getting confused/
 2 years ago

waterineyes Group TitleBest 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??
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
well the question in the book makes no sense
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
@sasogeek
 2 years ago

sasogeek Group TitleBest ResponseYou've already chosen the best response.0
certainly this is confusing, but why not use usubstitution for F(p) ?
 2 years ago

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

sasogeek Group TitleBest ResponseYou've already chosen the best response.0
\(let \ u=F(p)\) \(\large \frac{du}{dp}=F'(p)\) \(\large dp =\frac{du}{F'(p)} \) \[\int\limits_{p}^{\infty}u \ \frac{du}{F'(p)}\]
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
im not sure why you'd do that?
 2 years ago

sasogeek Group TitleBest 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?
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
differential equations; laplace transforms
 2 years ago

sasogeek Group TitleBest 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 :)
 2 years ago

UnkleRhaukus Group TitleBest 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
 2 years ago

UnkleRhaukus Group TitleBest 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
 2 years ago

sasogeek Group TitleBest ResponseYou've already chosen the best response.0
you could ask satellite73 or amistre when they get online....
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
@amistre64
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
yeah, i looked at this earlier and dont have anything pertinent to add to it :/ srry
 2 years ago
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