integral from 0 to 1 of-6x(x^2-2)^4

Lösung

\int_{0}^{1} - 6 x (x^{2} - 2)^{4} d x

- \frac{93}{5}

Dezimale

- 18.6

Schritte zur Lösung

\int_{0}^{1} - 6 x (x^{2} - 2)^{4} d x

Entferne die Konstante:

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

= - 6 \cdot \int_{0}^{1} x (x^{2} - 2)^{4} d x

Wende U-Substitution an

= - 6 \cdot \int_{- 2}^{- 1} \frac{u ^{4}}{2} d u

Entferne die Konstante:

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

= - 6 \cdot \frac{1}{2} \cdot \int_{- 2}^{- 1} u^{4} d u

Wende die Potenzregel an

= - 6 \cdot \frac{1}{2} [\frac{u ^{5}}{5}]_{- 2}^{- 1}

Vereinfache

- 6 \cdot \frac{1}{2} [\frac{u ^{5}}{5}]_{- 2}^{- 1} : - 3 [\frac{u ^{5}}{5}]_{- 2}^{- 1}

= - 3 [\frac{u ^{5}}{5}]_{- 2}^{- 1}

Berechne die Grenzen:

\frac{31}{5}

= - 3 \cdot \frac{31}{5}

Vereinfache

= - \frac{93}{5}

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