integral from 1 to 4 of xe^{2x}

Lösung

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

\frac{7 e ^{8} - e ^{2}}{4}

Dezimale

5214.82921 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{2}^{8} \frac{e ^{u} u}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{2}^{8} e^{u} u d u

Wende die partielle Integration an

= \frac{1}{4} [e^{u} u - \int e^{u} d u]_{2}^{8}

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

= \frac{1}{4} [e^{u} u - e^{u}]_{2}^{8}

Berechne die Grenzen:

7 e^{8} - e^{2}

= \frac{1}{4} (7 e^{8} - e^{2})

Vereinfache

= \frac{7 e ^{8} - e ^{2}}{4}

\int_{1}^{2} \frac{3}{7} x^{2} d x

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

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