integral from 3 to 8 of xe^{x^2}

Lösung

\int_{3}^{8} x e^{x^{2}} d x

\frac{e ^{64} - e ^{9}}{2}

Dezimale

3.11757 E 27

Schritte zur Lösung

\int_{3}^{8} x e^{x^{2}} d x

Wende U-Substitution an

= \int_{9}^{64} \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_{9}^{64} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [e^{u}]_{9}^{64}

Berechne die Grenzen:

e^{64} - e^{9}

= \frac{1}{2} (e^{64} - e^{9})

Vereinfache

= \frac{e ^{64} - e ^{9}}{2}

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