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Beliebt Rechnen >

integral from 0 to 1 of 6e^{3x}

Lösung

\int_{0}^{1} 6 e^{3 x} d x

Lösung

2 (e^{3} - 1)

+1

Dezimale

38.17107 \dots

Schritte zur Lösung

\int_{0}^{1} 6 e^{3 x} d x

Entferne die Konstante:

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

= 6 \cdot \int_{0}^{1} e^{3 x} d x

Wende U-Substitution an

= 6 \cdot \int_{0}^{3} e^{u} \frac{1}{3} d u

Entferne die Konstante:

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

= 6 \cdot \frac{1}{3} \cdot \int_{0}^{3} e^{u} d u

Nutze das gemeinsame Integral :

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

= 6 \cdot \frac{1}{3} [e^{u}]_{0}^{3}

Vereinfache

6 \cdot \frac{1}{3} [e^{u}]_{0}^{3} : 2 [e^{u}]_{0}^{3}

= 2 [e^{u}]_{0}^{3}

Berechne die Grenzen:

e^{3} - 1

= 2 (e^{3} - 1)

Graph

Beliebte Beispiele

integral from 0 to 4 of 6-2x

\int_{0}^{4} 6 - 2 x d x

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\int_{- 2}^{5} (3 + x - 2 ∣ x ∣) d x

integral from 1 to 2 of 8x

\int_{1}^{2} 8 x d x

integral from 0 to 3 of (6+6y-y^2)

\int_{0}^{3} (6 + 6 y - y^{2}) d y

integral from-2 to 1 of x^3+x

\int_{- 2}^{1} x^{3} + x d x