integral from 0 to 1 of [e^{5x+3}]

Lösung

\int_{0}^{1} [e^{5 x + 3}] d x

\frac{e ^{8} - e ^{3}}{5}

Dezimale

592.17449 \dots

Schritte zur Lösung

\int_{0}^{1} e^{5 x + 3} d x

Wende U-Substitution an

= \int_{3}^{8} 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_{3}^{8} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{5} [e^{u}]_{3}^{8}

Berechne die Grenzen:

e^{8} - e^{3}

= \frac{1}{5} (e^{8} - e^{3})

Vereinfache

= \frac{e ^{8} - e ^{3}}{5}

\int_{- \infty}^{0} 1 3^{x} d x

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