integral from 2 to 4 of xe^{4x}

Lösung

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

\frac{15 e ^{16} - 7 e ^{8}}{16}

Dezimale

8329424.44385 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{8}^{16} \frac{e ^{u} u}{16} d u

Entferne die Konstante:

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

= \frac{1}{16} \cdot \int_{8}^{16} e^{u} u d u

Wende die partielle Integration an

= \frac{1}{16} [e^{u} u - \int e^{u} d u]_{8}^{16}

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

= \frac{1}{16} [e^{u} u - e^{u}]_{8}^{16}

Berechne die Grenzen:

15 e^{16} - 7 e^{8}

= \frac{1}{16} (15 e^{16} - 7 e^{8})

Vereinfache

= \frac{15 e ^{16} - 7 e ^{8}}{16}