Integral mean value theorem

**daudaudaudau** · Jun14-09, 08:11 PM

http://en.wikipedia.org/wiki/Mean_va...or_integration

Take a look at the Wikipedia proof. Now, wouldn't it be easier to prove it like this:
The ordinary mean value theorem says that
$LaTeX Code: G(b)-G(a)=(b-a)Gsingle-quote(\\xi) $

And the fundamental theorem of calculus says that
$LaTeX Code: G(b)-G(a)=\\int_a^b Gsingle-quote(x)dx $

So the conclusion is
$LaTeX Code: \\int_a^b Gsingle-quote(x)dx=(b-a)Gsingle-quote(\\xi) $

**Office_Shredder** · Jun15-09, 04:37 AM

You proved the case where $LaTeX Code: \\phi = 1$ identically. Notice the wikipedia proof covers a far broader case than you did.

Also, you probably used the mean value theorem to prove the fundamental theorem of calculus, so this is circular

**daudaudaudau** · Jun15-09, 03:35 PM

I see.