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Beliebt Rechnen >

integral from-1 to 1 of e^x-(x^2-1)

Lösung

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

Lösung

e - \frac{1}{e} + \frac{4}{3}

+1

Dezimale

3.68373 \dots

Schritte zur Lösung

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{- 1}^{1} e^{x} d x = e - \frac{1}{e}

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

= e - \frac{1}{e} - (- \frac{4}{3})

Vereinfache

= e - \frac{1}{e} + \frac{4}{3}

Graph

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