integral from 0 to 1 of e^{8x-7}

Lösung

\int_{0}^{1} e^{8 x - 7} d x

\frac{e ^{8} - 1}{8 e ^{7}}

Dezimale

0.33967 \dots

Schritte zur Lösung

\int_{0}^{1} e^{8 x - 7} d x

Wende U-Substitution an

= \int_{- 7}^{1} e^{u} \frac{1}{8} d u

Entferne die Konstante:

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

= \frac{1}{8} \cdot \int_{- 7}^{1} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{8} [e^{u}]_{- 7}^{1}

Berechne die Grenzen:

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

= \frac{1}{8} (e - \frac{1}{e ^{7}})

Vereinfache

= \frac{e ^{8} - 1}{8 e ^{7}}

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