integral from 0 to 6 of 1/3 xe^x

Lösung

\int_{0}^{6} \frac{1}{3} x e^{x} d x

\frac{5 e ^{6} + 1}{3}

Dezimale

672.71465 \dots

Schritte zur Lösung

\int_{0}^{6} \frac{1}{3} x e^{x} d x

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{0}^{6} x e^{x} d x

Wende die partielle Integration an

= \frac{1}{3} [e^{x} x - \int e^{x} d x]_{0}^{6}

\int e^{x} d x = e^{x}

= \frac{1}{3} [e^{x} x - e^{x}]_{0}^{6}

Berechne die Grenzen:

5 e^{6} + 1

= \frac{1}{3} (5 e^{6} + 1)

Vereinfache

= \frac{5 e ^{6} + 1}{3}

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