integral from 1 to sqrt(2 of)xe^{5x^2}

Lösung

\int_{1}^{2} x e^{5 x^{2}} d x

\frac{e ^{10} - e ^{5}}{10}

Dezimale

2187.80526 \dots

Schritte zur Lösung

\int_{1}^{2} x e^{5 x^{2}} d x

Wende U-Substitution an

= \int_{5}^{10} \frac{e ^{u}}{10} d u

Entferne die Konstante:

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

= \frac{1}{10} \cdot \int_{5}^{10} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{10} [e^{u}]_{5}^{10}

Berechne die Grenzen:

e^{10} - e^{5}

= \frac{1}{10} (e^{10} - e^{5})

Vereinfache

= \frac{e ^{10} - e ^{5}}{10}

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