integral from 0 to pi of 10xsin(x)

Lösung

\int_{0}^{π} 10 x sin (x) d x

10 π

Dezimale

31.41592 \dots

Schritte zur Lösung

\int_{0}^{π} 10 x sin (x) d x

Entferne die Konstante:

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

= 10 \cdot \int_{0}^{π} x sin (x) d x

Wende die partielle Integration an

= 10 [- x cos (x) - \int - cos (x) d x]_{0}^{π}

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

= 10 [- x cos (x) - (- sin (x))]_{0}^{π}

Vereinfache

= 10 [- x cos (x) + sin (x)]_{0}^{π}

Berechne die Grenzen:

π

= 10 π

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