Timeline for Conditional Integration of arbitrary function
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 9, 2019 at 9:14 | comment | added | Michael Wild | To be honest I am hoping that there is an obvious solution to this problem that I simply missed. I actually wrote a small program that numerically solves this problem, it is indeed very easy to find a solution. If you look at it graphically it's obvious how to get there. However the final application that this problem is a part of is quite a lot more involved, that's why an analytical solution would be very beneficial. | |
| Oct 9, 2019 at 2:29 | comment | added | Aaron Bergman | What sort of answer are you hoping for here? It seems unlikely that there is an analytic answer, but I suspect you could easily solve this numerically. Starting with $A$ sufficiently large to make the integral positive and then proceeding by bisection seems like it ought to work. | |
| Oct 8, 2019 at 15:45 | comment | added | Michael Wild | True, thanks, I edited the question to make it clearer. | |
| Oct 8, 2019 at 15:42 | history | edited | Michael Wild | CC BY-SA 4.0 |
added 36 characters in body
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| Oct 8, 2019 at 15:17 | comment | added | Daniele Tampieri | Despite you do not know a priori the demand $g(t)$ nor the irradiation $f(t)$, you may try to guess something more on their structure: otherwise the question is not well posed since, strictly speaking, $g$ and $f$ could be non-integrable. For example, considering that the solar irradiation during the day brings only a finite energy to a given unit surface, you may assume a finite energy i.e. $L^2$ condition to hold for it, i.e. $$ \int_0^{T_\mathrm{day}}\!\! |f(t)|^2\mathrm{d} t\le\infty $$ And similar conditions may also hold for $g$. | |
| Oct 8, 2019 at 15:05 | review | First posts | |||
| Oct 8, 2019 at 18:42 | |||||
| Oct 8, 2019 at 15:00 | history | asked | Michael Wild | CC BY-SA 4.0 |