integral from 0 to 1 of e^x(x^2+x)

Lösung

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

e - 1

Dezimale

1.71828 \dots

Schritte zur Lösung

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

Multipliziere aus

e^{x} (x^{2} + x) : e^{x} x^{2} + e^{x} x

= \int_{0}^{1} e^{x} x^{2} + e^{x} x 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_{0}^{1} e^{x} x^{2} d x + \int_{0}^{1} e^{x} x d x

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

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

= e - 2 + 1

Vereinfache

= e - 1

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