integral from 0 to 1 of e^{tx}

Lösung

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

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

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{t} \frac{e ^{u}}{t} d u

Entferne die Konstante:

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

= \frac{1}{t} \cdot \int_{0}^{t} e^{u} d u

Nutze das gemeinsame Integral :

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

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

Vereinfache

\frac{1}{t} [e^{u}]_{0}^{t} : \frac{[ e ^{u} ] _{0}^{t}}{t}

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

Berechne die Grenzen:

e^{t} - 1

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

\int_{0}^{1} 4 x + 5 d x

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