integral from 0 to 1 of 4xe^{x^2}

Lösung

\int_{0}^{1} 4 x e^{x^{2}} d x

2 (e - 1)

Dezimale

3.43656 \dots

Schritte zur Lösung

\int_{0}^{1} 4 x e^{x^{2}} d x

Entferne die Konstante:

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

= 4 \cdot \int_{0}^{1} x e^{x^{2}} d x

Wende U-Substitution an

= 4 \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

= 4 \cdot \frac{1}{2} \cdot \int_{0}^{1} e^{u} d u

Nutze das gemeinsame Integral :

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

= 4 \cdot \frac{1}{2} [e^{u}]_{0}^{1}

Vereinfache

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

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

Berechne die Grenzen:

e - 1

= 2 (e - 1)

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