# Thread: prove that differentiation and integration are inverse functions??

4. ## Re: prove that differentiation and integration are inverse functions??

Originally Posted by mpx86
$f'(c) = \frac{{f(b) - f(a)}}{{b - a}}\left( {b - a} \right)\$/extract_itex] $f'(c)\left( {b - a} \right) = f(b) - f(a)\\$ doesnt this imply this $\left( {b - a} \right)f'(c) = F'(b) - F'(a){\rm{where}}F'(x) = f(x)$ You're right, it does not imply that. But that is NOT what I wrote. Read it properly! 5. ## Re: prove that differentiation and integration are inverse functions?? how can $\left( {b - a} \right)f'(c) = F'(b) - F'(a){\rm{where}}F'(x) = f(x)$ implies $\[\left( {b - a} \right)f(c){\rm{ }} = F(b) - F(a){\rm{where}}F'(x) = f(x)$$

sorry but i cant get this step ...........

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# integration inverse of differentiation proofs

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