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Beliebt Rechnen >

integral from-3 to 3 of 1/2 (81-x^4)

Lösung

\int_{- 3}^{3} \frac{1}{2} (81 - x^{4}) d x

Lösung

\frac{972}{5}

+1

Dezimale

194.4

Schritte zur Lösung

\int_{- 3}^{3} \frac{1}{2} (81 - x^{4}) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{- 3}^{3} 81 - x^{4} 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

= \frac{1}{2} (\int_{- 3}^{3} 81 d x - \int_{- 3}^{3} x^{4} d x)

\int_{- 3}^{3} 81 d x = 486

\int_{- 3}^{3} x^{4} d x = \frac{486}{5}

= \frac{1}{2} (486 - \frac{486}{5})

Vereinfache

\frac{1}{2} (486 - \frac{486}{5}) : \frac{972}{5}

= \frac{972}{5}

Graph

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