Prove that if f' and g' are continuous on a line interval [a,b] then

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- Apr 26th 2008, 09:27 AMmatty888Functions
Prove that if f' and g' are continuous on a line interval [a,b] then

http://www.cramster.com/Answer-Board...6080265979.gif - Apr 26th 2008, 09:29 AMMathstud28
- Apr 26th 2008, 09:32 AMMoo
Hello,

Mathstud : I think he wants to demonstrate it :p

$\displaystyle \int_a^b f(x)g'(x)dx=? f(x)g(x)|_a^b -\int_a^b g'(x)f(x) dx$

Consider f(x)g(x)

$\displaystyle f(x)g(x)|_a^b = \int_a^b \left(f(x)g(x) \right)' dx$

What is the derivative for $\displaystyle f(x)g(x)$? ;)

Then by using the linearity of the integral, you'll get the result.