integral from 2 to 3 of (x^2-4)^2x

Lösung

\int_{2}^{3} (x^{2} - 4)^{2} x d x

\frac{125}{6}

Dezimale

20.83333 \dots

Schritte zur Lösung

\int_{2}^{3} (x^{2} - 4)^{2} x d x

Multipliziere aus

(x^{2} - 4)^{2} x : x^{5} - 8 x^{3} + 16 x

= \int_{2}^{3} x^{5} - 8 x^{3} + 16 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_{2}^{3} x^{5} d x - \int_{2}^{3} 8 x^{3} d x + \int_{2}^{3} 16 x d x

\int_{2}^{3} x^{5} d x = \frac{665}{6}

\int_{2}^{3} 8 x^{3} d x = 130

\int_{2}^{3} 16 x d x = 40

= \frac{665}{6} - 130 + 40

Vereinfache

\frac{665}{6} - 130 + 40 : \frac{125}{6}

= \frac{125}{6}

\int_{1}^{2} (6 x^{5} - 3 x^{2} + 2 x) d x

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