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

Lösung

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

e^{4} - e

Dezimale

51.87986 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

= 2 \cdot \int_{1}^{2} x e^{x^{2}} d x

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

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

Vereinfache

2 \cdot \frac{1}{2} [e^{u}]_{1}^{4} : [e^{u}]_{1}^{4}

= [e^{u}]_{1}^{4}

Berechne die Grenzen:

e^{4} - e

= e^{4} - e

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