integral from-2 to-1 of 2x(7-x^2)^3

Lösung

\int_{- 2}^{- 1} 2 x (7 - x^{2})^{3} d x

- \frac{1215}{4}

Dezimale

- 303.75

Schritte zur Lösung

\int_{- 2}^{- 1} 2 x (7 - 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_{- 2}^{- 1} x (7 - x^{2})^{3} d x

Wende U-Substitution an

= 2 \cdot \int_{3}^{6} - \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_{3}^{6} u^{3} d u)

Wende die Potenzregel an

= 2 (- \frac{1}{2} [\frac{u ^{4}}{4}]_{3}^{6})

Vereinfache

2 (- \frac{1}{2} [\frac{u ^{4}}{4}]_{3}^{6}) : - [\frac{u ^{4}}{4}]_{3}^{6}

= - [\frac{u ^{4}}{4}]_{3}^{6}

Berechne die Grenzen:

\frac{1215}{4}

= - \frac{1215}{4}

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