integral from-1 to 0 of 1cos(npix)

Lösung

\int_{- 1}^{0} 1 cos (nπ x) d x

0

Schritte zur Lösung

\int_{- 1}^{0} 1 \cdot cos (nπ x) d x

Wende die partielle Integration an

= [x cos (πn x) - \int - πn x sin (πn x) d x]_{- 1}^{0}

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

= [x cos (πn x) - (x cos (πn x) - \frac{1}{πn} sin (πn x))]_{- 1}^{0}

Vereinfache

= [\frac{1}{πn} sin (πn x)]_{- 1}^{0}

Berechne die Grenzen:

0

= 0