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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{e ^{12} - e ^{6}}{3}

+1

Dezimale

54117.12087 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \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

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

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

e^{12} - e^{6}

= \frac{1}{3} (e^{12} - e^{6})

Vereinfache

= \frac{e ^{12} - e ^{6}}{3}

Graph

Beliebte Beispiele

integral from 3 to 4 of 3x^2

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

integral from 0 to t of (t-x)^3sin(x)

\int_{0}^{t} (t - x)^{3} sin (x) d x

integral from 0 to 2 of (-1/2 x+1)

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

integral from 0 to 2 of-1

\int_{0}^{2} - 1 d x

integral from 1 to 8 of 6

\int_{1}^{8} 6 d x