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

Lösung

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

\frac{11 e ^{12} - e ^{2}}{4}

Dezimale

447573.82913 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{2}^{12} \frac{e ^{u} u}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{2}^{12} e^{u} u d u

Wende die partielle Integration an

= \frac{1}{4} [e^{u} u - \int e^{u} d u]_{2}^{12}

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

= \frac{1}{4} [e^{u} u - e^{u}]_{2}^{12}

Berechne die Grenzen:

11 e^{12} - e^{2}

= \frac{1}{4} (11 e^{12} - e^{2})

Vereinfache

= \frac{11 e ^{12} - e ^{2}}{4}