- #1
Conductivity
- 87
- 3
I have seen the wikipedia's proof which can be found here: https://proofwiki.org/wiki/Integration_by_Substitution
However sometimes, we have problems where you have a ##d(x)## times ## f(g(x))## times g prime of x where we use substitution and it works but the proof didn't prove this condition..
I was wondering if you can prove why it works through infinite sums like for example
##( f(g(x)) g^{'}(x) dx + f(g(x+dx)) g^{'}(x+dx) dx + ... ) ##
If I can change that to this
##( f(y) dy + f(y+dy) dy + ... ## where you set y = g(x)
It would statisfy me.. But is it possible to prove it using this?
However sometimes, we have problems where you have a ##d(x)## times ## f(g(x))## times g prime of x where we use substitution and it works but the proof didn't prove this condition..
I was wondering if you can prove why it works through infinite sums like for example
##( f(g(x)) g^{'}(x) dx + f(g(x+dx)) g^{'}(x+dx) dx + ... ) ##
If I can change that to this
##( f(y) dy + f(y+dy) dy + ... ## where you set y = g(x)
It would statisfy me.. But is it possible to prove it using this?