integral from 0 to 3 of e^{x/3}(x^2+2x)

Lösung

\int_{0}^{3} e^{\frac{x}{3}} (x^{2} + 2 x) d x

27 e - 36

Dezimale

37.39360 \dots

Schritte zur Lösung

\int_{0}^{3} e^{\frac{x}{3}} (x^{2} + 2 x) d x

Multipliziere aus

e^{\frac{x}{3}} (x^{2} + 2 x) : e^{\frac{x}{3}} x^{2} + 2 e^{\frac{x}{3}} x

= \int_{0}^{3} e^{\frac{x}{3}} x^{2} + 2 e^{\frac{x}{3}} 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}^{3} e^{\frac{x}{3}} x^{2} d x + \int_{0}^{3} 2 e^{\frac{x}{3}} x d x

\int_{0}^{3} e^{\frac{x}{3}} x^{2} d x = 27 e - 54

\int_{0}^{3} 2 e^{\frac{x}{3}} x d x = 18

= 27 e - 54 + 18

Vereinfache

= 27 e - 36

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