integral from 1 to 2 of e^{3t}

Lösung

\int_{1}^{2} e^{3 t} d t

\frac{e ^{6} - e ^{3}}{3}

Dezimale

127.78108 \dots

Schritte zur Lösung

\int_{1}^{2} e^{3 t} d t

Wende U-Substitution an

= \int_{3}^{6} e^{u} \frac{1}{3} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{3}^{6} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{3} [e^{u}]_{3}^{6}

Berechne die Grenzen:

e^{6} - e^{3}

= \frac{1}{3} (e^{6} - e^{3})

Vereinfache

= \frac{e ^{6} - e ^{3}}{3}

\int_{0}^{2} x + 3 d x

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