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Beliebt Rechnen >

integral from 2 to 4 of 3e^{3x}

Lösung

\int_{2}^{4} 3 e^{3 x} d x

Lösung

e^{12} - e^{6}

+1

Dezimale

162351.36262 \dots

Schritte zur Lösung

\int_{2}^{4} 3 e^{3 x} d x

Entferne die Konstante:

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

= 3 \cdot \int_{2}^{4} e^{3 x} d x

Wende U-Substitution an

= 3 \cdot \int_{6}^{12} e^{u} \frac{1}{3} d u

Entferne die Konstante:

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

= 3 \cdot \frac{1}{3} \cdot \int_{6}^{12} e^{u} d u

Nutze das gemeinsame Integral :

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

= 3 \cdot \frac{1}{3} [e^{u}]_{6}^{12}

Vereinfache

3 \cdot \frac{1}{3} [e^{u}]_{6}^{12} : [e^{u}]_{6}^{12}

= [e^{u}]_{6}^{12}

Berechne die Grenzen:

e^{12} - e^{6}

= e^{12} - e^{6}

Graph

Beliebte Beispiele

derivative of 6e^x

\frac{d}{d x} (6 e^{x})

limit as x approaches 1 of 3x+1

x \to 1 lim (3 x + 1)

integral of x(ln(x))^3

\int x (ln (x))^{3} d x

integral of (e^{3x})/(1+e^x)

\int \frac{e ^{3 x}}{1 + e ^{x}} d x

limit as x approaches 3 of x^2+3x-1

x \to 3 lim (x^{2} + 3 x - 1)