integral from 0 to 1 of xe^{(x^2-1)}

Lösung

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

\frac{e - 1}{2 e}

Dezimale

0.31606 \dots

Schritte zur Lösung

\int_{0}^{1} x e^{x^{2} - 1} d x

Wende U-Substitution an

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

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

1 - \frac{1}{e}

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

Vereinfache

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

\int_{0}^{5} t i + t^{2} j + t^{3} k d x

\int_{0}^{2} x^{6} J_{3} (2 x) d x

\int_{- 1}^{2} (x^{2} - 2 x) d x

\int_{3}^{4} \frac{1}{x - 2 x} d x

\int_{0}^{4} \frac{x + 1}{x ^{2} + 2 x + 1} d x