integral from 0 to 3 of 15e^{3x}

Lösung

\int_{0}^{3} 15 e^{3 x} d x

5 (e^{9} - 1)

Dezimale

40510.41963 \dots

Schritte zur Lösung

\int_{0}^{3} 15 e^{3 x} d x

Entferne die Konstante:

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

= 15 \cdot \int_{0}^{3} e^{3 x} d x

Wende U-Substitution an

= 15 \cdot \int_{0}^{9} e^{u} \frac{1}{3} d u

Entferne die Konstante:

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

= 15 \cdot \frac{1}{3} \cdot \int_{0}^{9} e^{u} d u

Nutze das gemeinsame Integral :

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

= 15 \cdot \frac{1}{3} [e^{u}]_{0}^{9}

Vereinfache

15 \cdot \frac{1}{3} [e^{u}]_{0}^{9} : 5 [e^{u}]_{0}^{9}

= 5 [e^{u}]_{0}^{9}

Berechne die Grenzen:

e^{9} - 1

= 5 (e^{9} - 1)

\int_{0}^{1} (x + 2) d x

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