Math Help - Functions

1. Functions

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

2. 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

3. Hello,

Mathstud : I think he wants to demonstrate it

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

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.