# Math Help - Green's formula

1. ## Green's formula

Find by three methods a Green's formula for the operator $B=\frac{d^4}{dx^4}$.

$\displaystyle\int_a^bf^{(4)}g \ dx$

Need a lot of help here, thanks.

2. My hint was to use integration by parts 4 times.

$\displaystyle f'''g-fg'''+f'g''-f''g'+\int_a^bfg^{(4)}dx$

Now, it says notice that $B=A^2$ where $A=-\left(\frac{d^2}{dx^2}\right)$.

Show that $f'''g-fg'''$ is a derivative [analogous to formula (4.6.1)]

4.6.1:
$f''g-fg''=\frac{d}{dx}(f'g-fg')$

Not sure how to do that, but I assume it isn't too difficult.