integral from 0 to pi of 3x

Lösung

\int_{0}^{π} 3 x d x

\frac{3 π ^{2}}{2}

Dezimale

14.80440 \dots

Schritte zur Lösung

\int_{0}^{π} 3 x d x

Entferne die Konstante:

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

= 3 \cdot \int_{0}^{π} x d x

Wende die Potenzregel an

= 3 [\frac{x ^{2}}{2}]_{0}^{π}

Berechne die Grenzen:

\frac{π ^{2}}{2}

= 3 \cdot \frac{π ^{2}}{2}

Vereinfache

= \frac{3 π ^{2}}{2}

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