integral from-1 to 1 of e^{3x}

Lösung

\int_{- 1}^{1} e^{3 x} d x

\frac{e ^{6} - 1}{3 e ^{3}}

Dezimale

6.67858 \dots

Schritte zur Lösung

\int_{- 1}^{1} e^{3 x} d x

Wende U-Substitution an

= \int_{- 3}^{3} e^{u} \frac{1}{3} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{- 3}^{3} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{3} [e^{u}]_{- 3}^{3}

Berechne die Grenzen:

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

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

Vereinfache

= \frac{e ^{6} - 1}{3 e ^{3}}

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