Prove that if f' and g' are continuous on a line interval [a,b] then
Hello,
Mathstud : I think he wants to demonstrate it
$\displaystyle \int_a^b f(x)g'(x)dx=? f(x)g(x)|_a^b -\int_a^b g'(x)f(x) dx$
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.