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I would appreciate if somebody could help me with the following problem:

Please explain how to do this proof ? $$ $$ $G(x)$ : monotone increasing function and $G(x)\geq 0$ , $G'(x),f(x)$ : conti-function on $[a,b]$ then exist $c\in (a,b)$ s.t $$ \int_{a}^{b}f(x)G(x)dx=G(a)\int_{a}^{c}f(x)dx$$

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Is this correct? What if $G(a)=0$? Take $f(x)=g(x)=x$ and $[a,b]=[0,1]$. –  Maesumi Feb 20 '13 at 12:34
    
We do have $\int_a^b f(x)g(x)dx= g(c)\int_a^bf(x)dx$ though. –  Maesumi Feb 20 '13 at 12:36

1 Answer 1

up vote 1 down vote accepted

Hint: See Bonnet's second mean value theorem for details.

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@wildcow: If you think the hint is not appropriate, leave it alone. I mean, you don't have to accept it, or even vote it. I just added the proper link. Please make it unaccepted it to be deleted. I think, it should have added as an comment above. Thanks. –  B. S. Feb 20 '13 at 6:58
    
I'm sorry.Or have been, it does not help –  Young Feb 20 '13 at 10:05
    
@wildcow: That's Ok. :-) so please make it unaccepted. I want to make it as a comment. ;) –  B. S. Feb 20 '13 at 10:11
    
Will not be able to take advantage of the content of the site has given you. Thank you. Sorry my English is not very good. –  Young Feb 20 '13 at 10:57
    
+1 I think you may have just capped for the day (in upvotes!) –  amWhy Feb 20 '13 at 17:04

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