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Beliebt Rechnen >

integral of xcos((nxpi)/l)

Lösung

\int x cos (\frac{n x π}{l}) d x

Lösung

l \frac{1}{πn} x sin (\frac{πn x}{l}) + l \frac{l}{π ^{2} n ^{2}} cos (\frac{πn x}{l}) + C

Schritte zur Lösung

\int x cos (\frac{n x π}{l}) d x

Wende die partielle Integration an

= l \frac{1}{πn} x sin (\frac{πn x}{l}) - \int l \frac{1}{πn} sin (\frac{πn x}{l}) d x

\int l \frac{1}{πn} sin (\frac{πn x}{l}) d x = - l \frac{l}{π ^{2} n ^{2}} cos (\frac{πn x}{l})

= l \frac{1}{πn} x sin (\frac{πn x}{l}) - (- l \frac{l}{π ^{2} n ^{2}} cos (\frac{πn x}{l}))

Vereinfache

= l \frac{1}{πn} x sin (\frac{πn x}{l}) + l \frac{l}{π ^{2} n ^{2}} cos (\frac{πn x}{l})

Füge eine Konstante zur Lösung hinzu

= l \frac{1}{πn} x sin (\frac{πn x}{l}) + l \frac{l}{π ^{2} n ^{2}} cos (\frac{πn x}{l}) + C

Graph

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