integral from 1 to 2 of xe^{3x^2}

Lösung

\int_{1}^{2} x e^{3 x^{2}} d x

\frac{e ^{12} - e ^{3}}{6}

Dezimale

27122.45098 \dots

Schritte zur Lösung

\int_{1}^{2} x e^{3 x^{2}} d x

Wende U-Substitution an

= \int_{3}^{12} \frac{e ^{u}}{6} d u

Entferne die Konstante:

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

= \frac{1}{6} \cdot \int_{3}^{12} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{6} [e^{u}]_{3}^{12}

Berechne die Grenzen:

e^{12} - e^{3}

= \frac{1}{6} (e^{12} - e^{3})

Vereinfache

= \frac{e ^{12} - e ^{3}}{6}

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