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

Lösung

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

\frac{e - 1}{2}

Dezimale

0.85914 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{1} \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}^{1} e^{u} d u

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

e - 1

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

Vereinfache

= \frac{e - 1}{2}

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