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

Lösung

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

\frac{3 ( 15 e ^{16} + 1 )}{16}

Dezimale

24992186.02642 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende U-Substitution an

= 3 \cdot \int_{0}^{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

= 3 \cdot \frac{1}{16} \cdot \int_{0}^{16} e^{u} u d u

Wende die partielle Integration an

= 3 \cdot \frac{1}{16} [e^{u} u - \int e^{u} d u]_{0}^{16}

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

= 3 \cdot \frac{1}{16} [e^{u} u - e^{u}]_{0}^{16}

Vereinfache

3 \cdot \frac{1}{16} [e^{u} u - e^{u}]_{0}^{16} : \frac{3}{16} [e^{u} u - e^{u}]_{0}^{16}

= \frac{3}{16} [e^{u} u - e^{u}]_{0}^{16}

Berechne die Grenzen:

15 e^{16} + 1

= \frac{3}{16} (15 e^{16} + 1)

Vereinfache

= \frac{3 ( 15 e ^{16} + 1 )}{16}

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