integral from-1 to 2 of x^2(x^3+2)^2

Lösung

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

111

Schritte zur Lösung

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

Multipliziere aus

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

= \int_{- 1}^{2} x^{8} + 4 x^{5} + 4 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_{- 1}^{2} x^{8} d x + \int_{- 1}^{2} 4 x^{5} d x + \int_{- 1}^{2} 4 x^{2} d x

\int_{- 1}^{2} x^{8} d x = 57

\int_{- 1}^{2} 4 x^{5} d x = 42

\int_{- 1}^{2} 4 x^{2} d x = 12

= 57 + 42 + 12

Vereinfache

= 111

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