integral from 0 to 2 of (x^2e^{x^3})

Lösung

\int_{0}^{2} (x^{2} e^{x^{3}}) d x

\frac{e ^{8} - 1}{3}

Dezimale

993.31932 \dots

Schritte zur Lösung

\int_{0}^{2} x^{2} e^{x^{3}} d x

Wende U-Substitution an

= \int_{0}^{8} \frac{e ^{u}}{3} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{0}^{8} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{3} [e^{u}]_{0}^{8}

Berechne die Grenzen:

e^{8} - 1

= \frac{1}{3} (e^{8} - 1)

Vereinfache

= \frac{e ^{8} - 1}{3}

\int_{0}^{2} \frac{4 x}{2 + x ^{2}} d x

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