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Beliebt Rechnen >

integral from 1 to 4 of 4e^{sqrt(x)}

Lösung

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

Lösung

8 e^{2}

+1

Dezimale

59.11244 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

= 4 \cdot 2 [e^{u} u - \int e^{u} d u]_{1}^{2}

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

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

Vereinfache

= 8 [e^{u} u - e^{u}]_{1}^{2}

Berechne die Grenzen:

e^{2}

= 8 e^{2}

Graph

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