integral from-5 to 0 of cos((npix)/5)

Lösung

\int_{- 5}^{0} cos (\frac{nπ x}{5}) d x

0

Schritte zur Lösung

\int_{- 5}^{0} cos (\frac{nπ x}{5}) d x

Wende die partielle Integration an

= [x cos (\frac{πn x}{5}) - \int - \frac{πn}{5} x sin (\frac{πn x}{5}) d x]_{- 5}^{0}

\int - \frac{πn}{5} x sin (\frac{πn x}{5}) d x = x cos (\frac{πn x}{5}) - \frac{5}{πn} sin (\frac{πn x}{5})

= [x cos (\frac{πn x}{5}) - (x cos (\frac{πn x}{5}) - \frac{5}{πn} sin (\frac{πn x}{5}))]_{- 5}^{0}

Vereinfache

= [\frac{5}{πn} sin (\frac{πn x}{5})]_{- 5}^{0}

Berechne die Grenzen:

0

= 0

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