# Functions

• April 26th 2008, 09:27 AM
matty888
Functions
Prove that if f' and g' are continuous on a line interval [a,b] then
• April 26th 2008, 09:29 AM
Mathstud28
Quote:

Originally Posted by matty888
Prove that if f' and g' are continuous on a line interval [a,b] then

This is just the definition of integration by parts of a definite integral
• April 26th 2008, 09:32 AM
Moo
Hello,

Mathstud : I think he wants to demonstrate it :p

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

Consider f(x)g(x)

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

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

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