- 1.PNG (25.94 KiB) 728 keer bekeken
\( \eta\)
die voldoet aan de randvoorwaarden en bekom op:\( \int_0^1 \frac{d^4 u}{dx^4} \eta\ \mbox{d}x = \int_0^1 f \eta\ \mbox{d}x \)
Partieel integratie:\( \int_0^1 \frac{d^4 u}{dx^4} \eta\ \mbox{d}x = \frac{d^3 u}{dx^3} \eta\ |_0^1 - \int_0^1 \frac{d \eta}{dx} \frac{d^3 u}{dx^3}\ \mbox{d}x \)
\(= \eta|_1 - \frac{d \eta}{dx} \frac{d^2u}{dx^2}|_0^1 - \int \frac{d^2 \eta}{dx^2} \frac{d^2 u}{dx^2}\ \mbox{d}x \)
\(= \eta|_1 - \int \frac{d^2 \eta}{dx^2} \frac{d^2 u}{dx^2}\ \mbox{d}x \)
Is dit correct?
