integral from 0 to 2 of e^{sqrt(x)}

Lösung

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

2 (2 e^{2} - e^{2} + 1)

Dezimale

5.40752 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{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

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

Wende die partielle Integration an

= 2 [e^{u} u - \int e^{u} d u]_{0}^{2}

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

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

Berechne die Grenzen:

2 e^{2} - e^{2} + 1

= 2 (2 e^{2} - e^{2} + 1)

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