- #1

- 76

- 0

I have to show that if the derivate f'(x) of a generalized function f(x) is defined by the sequence f'_n(x) where f(x) is defined

[tex]f_n(x)[\tex]

then

[tex]\int_{-\infty}^{\infty}f'(x)F(x) dx = - \int_{-\infty}^{\infty}f(x)F'(x) dx [/tex]

I use the limits for generalized functions and get

[tex]lim_{n \to \infty} \int_{-\infty}^{\infty}f'_n(x)F(x) dx = - \int_{-\infty}^{\infty}f_n(x)F'(x) dx [/tex]

which should show the above - I am a liltte confused where the minus sign comes from?

[tex]- \int_{-\infty}^{\infty}f(x)F'(x) dx [/tex]

Any help appreciated - thanks in advance