integral from 0 to 1 of e^{x^2}2x

Lösung

\int_{0}^{1} e^{x^{2}} 2 x d x

e - 1

Dezimale

1.71828 \dots

Schritte zur Lösung

\int_{0}^{1} e^{x^{2}} \cdot 2 x d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{1} e^{x^{2}} x d x

Wende U-Substitution an

= 2 \cdot \int_{0}^{1} \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_{0}^{1} e^{u} d u

Nutze das gemeinsame Integral :

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

= 2 \cdot \frac{1}{2} [e^{u}]_{0}^{1}

Vereinfache

2 \cdot \frac{1}{2} [e^{u}]_{0}^{1} : [e^{u}]_{0}^{1}

= [e^{u}]_{0}^{1}

Berechne die Grenzen:

e - 1

= e - 1

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