integral from-3 to-1 of 2x(5-x^2)^3

Lösung

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

0

Schritte zur Lösung

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

Entferne die Konstante:

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

= 2 \cdot \int_{- 3}^{- 1} x (5 - x^{2})^{3} d x

Wende U-Substitution an

= 2 \cdot \int_{- 4}^{4} - \frac{u ^{3}}{2} d u

Entferne die Konstante:

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

= 2 (- \frac{1}{2} \cdot \int_{- 4}^{4} u^{3} d u)

Wende die Potenzregel an

= 2 (- \frac{1}{2} [\frac{u ^{4}}{4}]_{- 4}^{4})

Vereinfache

2 (- \frac{1}{2} [\frac{u ^{4}}{4}]_{- 4}^{4}) : - [\frac{u ^{4}}{4}]_{- 4}^{4}

= - [\frac{u ^{4}}{4}]_{- 4}^{4}

Berechne die Grenzen:

0

= - 0

Vereinfache

= 0

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