integral from 0 to 1 of e^{5x-4}

Lösung

\int_{0}^{1} e^{5 x - 4} d x

\frac{e ^{5} - 1}{5 e ^{4}}

Dezimale

0.53999 \dots

Schritte zur Lösung

\int_{0}^{1} e^{5 x - 4} d x

Wende U-Substitution an

= \int_{- 4}^{1} e^{u} \frac{1}{5} d u

Entferne die Konstante:

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

= \frac{1}{5} \cdot \int_{- 4}^{1} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{5} [e^{u}]_{- 4}^{1}

Berechne die Grenzen:

e - \frac{1}{e ^{4}}

= \frac{1}{5} (e - \frac{1}{e ^{4}})

Vereinfache

= \frac{e ^{5} - 1}{5 e ^{4}}

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