integral from 0 to 2 of (xe^{x^2})

Lösung

\int_{0}^{2} (x e^{x^{2}}) d x

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

Dezimale

26.79907 \dots

Schritte zur Lösung

\int_{0}^{2} x e^{x^{2}} d x

Wende U-Substitution an

= \int_{0}^{4} \frac{e ^{u}}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{4} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [e^{u}]_{0}^{4}

Berechne die Grenzen:

e^{4} - 1

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

Vereinfache

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

\int_{0}^{2 π} cos (m x) d x

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