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UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2in 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

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2as 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

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.0As we know that integration is independent of variable. You could use any variable of your choice. I'd go with the first one :)

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

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

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

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

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

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

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

waterineyes
 2 years ago
Best ResponseYou've already chosen the best response.0The 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??

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

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

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

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

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

sasogeek
 2 years ago
Best ResponseYou've already chosen the best response.0well 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?

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

sasogeek
 2 years ago
Best ResponseYou've already chosen the best response.0there 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 :)

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2but 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

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2i 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

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

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