integral from 1 to 2 of 6e^{6x}

Lösung

\int_{1}^{2} 6 e^{6 x} d x

e^{12} - e^{6}

Dezimale

162351.36262 \dots

Schritte zur Lösung

\int_{1}^{2} 6 e^{6 x} d x

Entferne die Konstante:

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

= 6 \cdot \int_{1}^{2} e^{6 x} d x

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

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

Vereinfache

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

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

Berechne die Grenzen:

e^{12} - e^{6}

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

d er i v a t i v e (2 x)^{6 x}

\int (ln (x))^{6} d x

\frac{d}{d x} ((x^{2} + 3) 4 - x^{2})

(cos^{3} (t))^{^{'}}

\frac{d}{d x} (sin (1000 x))