integral from 1 to e of xe^{2x^2-1}

Lösung

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

\frac{e ^{2 e^{2} - 1} - e}{4}

Dezimale

240822.40084 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{2 e^{2} - 1} \frac{e ^{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_{1}^{2 e^{2} - 1} e^{u} d u

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

e^{2 e^{2} - 1} - e

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

Vereinfache

= \frac{e ^{2 e^{2} - 1} - e}{4}

\int_{1}^{6} x^{2} - 2 x - 8 d x

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\int_{0}^{1} x^{2} - 4 x + 3 d x

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