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Beliebt Rechnen >

integral from-1 to 2 of xe^{6x}

Lösung

\int_{- 1}^{2} x e^{6 x} d x

Lösung

\frac{11 e ^{18} + 7}{36 e ^{6}}

+1

Dezimale

49730.63119 \dots

Schritte zur Lösung

\int_{- 1}^{2} x e^{6 x} d x

Wende U-Substitution an

= \int_{- 6}^{12} \frac{e ^{u} u}{36} d u

Entferne die Konstante:

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

= \frac{1}{36} \cdot \int_{- 6}^{12} e^{u} u d u

Wende die partielle Integration an

= \frac{1}{36} [e^{u} u - \int e^{u} d u]_{- 6}^{12}

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

= \frac{1}{36} [e^{u} u - e^{u}]_{- 6}^{12}

Berechne die Grenzen:

11 e^{12} + \frac{7}{e ^{6}}

= \frac{1}{36} (11 e^{12} + \frac{7}{e ^{6}})

Vereinfache

= \frac{11 e ^{18} + 7}{36 e ^{6}}

Graph

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