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Beliebt Rechnen >

integral from 0 to 1 of e^{(2x)/3}

Lösung

\int_{0}^{1} e^{\frac{2 x}{3}} d x

Lösung

\frac{3 ( e ^{\frac{2}{3}} - 1 )}{2}

+1

Dezimale

1.42160 \dots

Schritte zur Lösung

\int_{0}^{1} e^{\frac{2 x}{3}} d x

Wende U-Substitution an

= \int_{0}^{\frac{2}{3}} e^{u} \frac{3}{2} d u

Entferne die Konstante:

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

= \frac{3}{2} \cdot \int_{0}^{\frac{2}{3}} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{3}{2} [e^{u}]_{0}^{\frac{2}{3}}

Berechne die Grenzen:

e^{\frac{2}{3}} - 1

= \frac{3}{2} (e^{\frac{2}{3}} - 1)

Vereinfache

= \frac{3 ( e ^{\frac{2}{3}} - 1 )}{2}

Graph

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