integral from 0 to 4 of 6xe^{3x^2}

Lösung

\int_{0}^{4} 6 x e^{3 x^{2}} d x

e^{48} - 1

Dezimale

7.01674 E 20

Schritte zur Lösung

\int_{0}^{4} 6 x e^{3 x^{2}} d x

Entferne die Konstante:

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

= 6 \cdot \int_{0}^{4} x e^{3 x^{2}} d x

Wende U-Substitution an

= 6 \cdot \int_{0}^{48} \frac{e ^{u}}{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_{0}^{48} e^{u} d u

Nutze das gemeinsame Integral :

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

= 6 \cdot \frac{1}{6} [e^{u}]_{0}^{48}

Vereinfache

6 \cdot \frac{1}{6} [e^{u}]_{0}^{48} : [e^{u}]_{0}^{48}

= [e^{u}]_{0}^{48}

Berechne die Grenzen:

e^{48} - 1

= e^{48} - 1

\int_{0}^{1} x cos (a x) d x

\int_{1}^{4} 2 x^{2} + x d x

\int_{2}^{0} x^{3} - 3 x^{2} + 2 d x

\int_{2}^{3} \frac{1}{x ^{4} - x ^{2}} d x

\int_{0}^{l n (2)} e^{2 x} (5 - e) d x