integral from 0 to 1 of 3r^2e^{r^3}

Lösung

\int_{0}^{1} 3 r^{2} e^{r^{3}} d r

e - 1

Dezimale

1.71828 \dots

Schritte zur Lösung

\int_{0}^{1} 3 r^{2} e^{r^{3}} d r

Entferne die Konstante:

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

= 3 \cdot \int_{0}^{1} r^{2} e^{r^{3}} d r

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

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

Vereinfache

3 \cdot \frac{1}{3} [e^{u}]_{0}^{1} : [e^{u}]_{0}^{1}

= [e^{u}]_{0}^{1}

Berechne die Grenzen:

e - 1

= e - 1

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