integral from 1 to 4 of xe^{3x}

Lösung

\int_{1}^{4} x e^{3 x} d x

\frac{11 e ^{12} - 2 e ^{3}}{9}

Dezimale

198918.05939 \dots

Schritte zur Lösung

\int_{1}^{4} x e^{3 x} d x

Wende U-Substitution an

= \int_{3}^{12} \frac{e ^{u} u}{9} d u

Entferne die Konstante:

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

= \frac{1}{9} \cdot \int_{3}^{12} e^{u} u d u

Wende die partielle Integration an

= \frac{1}{9} [e^{u} u - \int e^{u} d u]_{3}^{12}

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

= \frac{1}{9} [e^{u} u - e^{u}]_{3}^{12}

Berechne die Grenzen:

11 e^{12} - 2 e^{3}

= \frac{1}{9} (11 e^{12} - 2 e^{3})

Vereinfache

= \frac{11 e ^{12} - 2 e ^{3}}{9}

\int_{0}^{1} x^{4} \cdot e^{- x} d x

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