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

Lösung

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

- e + 3

Dezimale

0.28171 \dots

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

= 1 - (e - 2)

Vereinfache

= - e + 3