integral from 0 to 1 of e^{14x-13}

Lösung

\int_{0}^{1} e^{14 x - 13} d x

\frac{e ^{14} - 1}{14 e ^{13}}

Dezimale

0.19416 \dots

Schritte zur Lösung

\int_{0}^{1} e^{14 x - 13} d x

Wende U-Substitution an

= \int_{- 13}^{1} e^{u} \frac{1}{14} d u

Entferne die Konstante:

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

= \frac{1}{14} \cdot \int_{- 13}^{1} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{14} [e^{u}]_{- 13}^{1}

Berechne die Grenzen:

e - \frac{1}{e ^{13}}

= \frac{1}{14} (e - \frac{1}{e ^{13}})

Vereinfache

= \frac{e ^{14} - 1}{14 e ^{13}}

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