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Beliebt Rechnen >

integral from 0 to 1 of 7xe^{x^2}

Lösung

\int_{0}^{1} 7 x e^{x^{2}} d x

Lösung

\frac{7 ( e - 1 )}{2}

+1

Dezimale

6.01398 \dots

Schritte zur Lösung

\int_{0}^{1} 7 x e^{x^{2}} d x

Entferne die Konstante:

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

= 7 \cdot \int_{0}^{1} x e^{x^{2}} d x

Wende U-Substitution an

= 7 \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

= 7 \cdot \frac{1}{2} \cdot \int_{0}^{1} e^{u} d u

Nutze das gemeinsame Integral :

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

= 7 \cdot \frac{1}{2} [e^{u}]_{0}^{1}

Vereinfache

7 \cdot \frac{1}{2} [e^{u}]_{0}^{1} : \frac{7}{2} [e^{u}]_{0}^{1}

= \frac{7}{2} [e^{u}]_{0}^{1}

Berechne die Grenzen:

e - 1

= \frac{7}{2} (e - 1)

Vereinfache

= \frac{7 ( e - 1 )}{2}

Graph

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