integral from 0 to 1 of x(e^x-1)

Lösung

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

\frac{1}{2}

Dezimale

0.5

Schritte zur Lösung

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

Wende die partielle Integration an

= [x (e^{x} - x) - \int e^{x} - x d x]_{0}^{1}

\int e^{x} - x d x = e^{x} - \frac{x ^{2}}{2}

= [x (e^{x} - x) - (e^{x} - \frac{x ^{2}}{2})]_{0}^{1}

Vereinfache

[x (e^{x} - x) - (e^{x} - \frac{x ^{2}}{2})]_{0}^{1} : [\frac{1}{2} (- x^{2} + 2 e^{x} x - 2 e^{x})]_{0}^{1}

= [\frac{1}{2} (- x^{2} + 2 e^{x} x - 2 e^{x})]_{0}^{1}

Berechne die Grenzen:

\frac{1}{2}

= \frac{1}{2}

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