integral from 0 to 2pi of 2xcos(x)

Lösung

\int_{0}^{2 π} 2 x cos (x) d x

0

Schritte zur Lösung

\int_{0}^{2 π} 2 x cos (x) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{2 π} x cos (x) d x

Wende die partielle Integration an

= 2 [x sin (x) - \int sin (x) d x]_{0}^{2 π}

\int sin (x) d x = - cos (x)

= 2 [x sin (x) - (- cos (x))]_{0}^{2 π}

Vereinfache

= 2 [x sin (x) + cos (x)]_{0}^{2 π}

Berechne die Grenzen:

0

= 2 \cdot 0

Vereinfache

= 0

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