integral from 0 to 1 of e^{10x-9}

Lösung

\int_{0}^{1} e^{10 x - 9} d x

\frac{e ^{10} - 1}{10 e ^{9}}

Dezimale

0.27181 \dots

Schritte zur Lösung

\int_{0}^{1} e^{10 x - 9} d x

Wende U-Substitution an

= \int_{- 9}^{1} e^{u} \frac{1}{10} d u

Entferne die Konstante:

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

= \frac{1}{10} \cdot \int_{- 9}^{1} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{10} [e^{u}]_{- 9}^{1}

Berechne die Grenzen:

e - \frac{1}{e ^{9}}

= \frac{1}{10} (e - \frac{1}{e ^{9}})

Vereinfache

= \frac{e ^{10} - 1}{10 e ^{9}}

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