integral from 0 to 2 of (t-1)e^{(t-1)^2}

Lösung

\int_{0}^{2} (t - 1) e^{(t - 1)^{2}} d t

0

Schritte zur Lösung

\int_{0}^{2} (t - 1) e^{(t - 1)^{2}} d t

Wende U-Substitution an

= \int_{- 1}^{1} e^{u^{2}} u d u

Wende die partielle Integration an

= [\frac{1}{2} e^{u^{2}} u^{2} - \int e^{u^{2}} u^{3} d u]_{- 1}^{1}

\int e^{u^{2}} u^{3} d u = \frac{1}{2} (e^{u^{2}} u^{2} - e^{u^{2}})

= [\frac{1}{2} e^{u^{2}} u^{2} - \frac{1}{2} (e^{u^{2}} u^{2} - e^{u^{2}})]_{- 1}^{1}

Vereinfache

[\frac{1}{2} e^{u^{2}} u^{2} - \frac{1}{2} (e^{u^{2}} u^{2} - e^{u^{2}})]_{- 1}^{1} : [\frac{1}{2} e^{u^{2}}]_{- 1}^{1}

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

Berechne die Grenzen:

0

= 0

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