Question

question about notation

Answer 1

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

Answer 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

Answer 3

As we know that integration is independent of variable. You could use any variable of your choice. I'd go with the first one :)

Answer 4

a?

Answer 5

yes

Answer 6

\[\int\limits_p^\infty F(a)\cdot\text da\]

Answer 7

\[\int\limits_p^\infty F(x)\cdot\text dx\]

Answer 8

\[\int\limits\limits_p^\infty F(mukushla)\cdot\text d(mukushla)\]

Answer 9

the notation is still troubling me

Answer 10

Where???

Answer 11

well i kinda had to change the question so i could answer it

Answer 12

\[\begin{align*}
\int\limits_p^\infty F(q)\cdot\text dq
&=\int\limits_p^\infty\int\limits_0^\infty f(x)e^{-qx}\cdot\text dx\cdot\text dq
\\&=\int\limits_0^\infty f(x)\int\limits_p^\infty e^{-qx}\cdot\text dq\cdot\text dx
\\&=\int\limits_0^\infty f(x)\left.\frac{e^{-qx}}{-x}\right|_p^\infty \cdot\text dx
\\&=\int\limits_0^\infty \frac{f(x)}xe^{-px}\cdot\text dx
\\&=\mathcal L\left\{\frac {f(x) }x \right\}
\end{align*}\]

Answer 13

do you understand why i am getting confused/

Answer 14

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??

Answer 15

well the question in the book makes no sense

Answer 16

@sasogeek

Answer 17

certainly this is confusing, but why not use u-substitution for F(p) ?

Answer 18

like this?

\[\begin{align*}
\int\limits_p^\infty F(p)\cdot\text dp\\
\text{let }u=p\\
\text du=\text dp\\
\\p=p\rightarrow u=u\\
p=\infty\rightarrow u=\infty\\
\\&=\int\limits_u^\infty F(u)\cdot\text du\\
\end{align*}\]

Answer 19

\(let \ u=F(p)\)
\(\large \frac{du}{dp}=F'(p)\)
\(\large dp =\frac{du}{F'(p)} \)

\[\int\limits_{p}^{\infty}u \ \frac{du}{F'(p)}\]

Answer 20

im not sure why you'd do that?

Answer 21

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?

Answer 22

differential equations; laplace transforms

Answer 23

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 :)

Answer 24

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

Answer 25

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

Answer 26

you could ask satellite73 or amistre when they get online....

Answer 27

@amistre64

Answer 28

yeah, i looked at this earlier and dont have anything pertinent to add to it :/ srry