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

Lösung

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

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

Dezimale

156.51902 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{7} 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_{0}^{7} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{7} [e^{u}]_{0}^{7}

Berechne die Grenzen:

e^{7} - 1

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

Vereinfache

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

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