integral of (x-pi)sin(nx)

Lösung

\int (x - π) sin (n x) d x

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

Schritte zur Lösung

\int (x - π) sin (n x) d x

Wende die partielle Integration an

= - \frac{1}{n} cos (n x) (x - π) - \int - \frac{1}{n} cos (n x) d x

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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