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Math Help - Green's formula

  1. #1
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    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.
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  2. #2
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    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.
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