integral from 0 to 1 of e^{7x-6}

Lösung

\int_{0}^{1} e^{7 x - 6} d x

\frac{e ^{7} - 1}{7 e ^{6}}

Dezimale

0.38797 \dots

Schritte zur Lösung

\int_{0}^{1} e^{7 x - 6} d x

Wende U-Substitution an

= \int_{- 6}^{1} e^{u} \frac{1}{7} d u

Entferne die Konstante:

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

= \frac{1}{7} \cdot \int_{- 6}^{1} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{7} [e^{u}]_{- 6}^{1}

Berechne die Grenzen:

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

= \frac{1}{7} (e - \frac{1}{e ^{6}})

Vereinfache

= \frac{e ^{7} - 1}{7 e ^{6}}

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