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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{21}{4} f

Schritte zur Lösung

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

Entferne die Konstante:

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

= f \cdot \int_{- 2}^{- 1} (1 + x^{2}) x d x

Multipliziere aus

(1 + x^{2}) x : x + x^{3}

= f \cdot \int_{- 2}^{- 1} x + x^{3} 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

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

\int_{- 2}^{- 1} x d x = - \frac{3}{2}

\int_{- 2}^{- 1} x^{3} d x = - \frac{15}{4}

= f (- \frac{3}{2} - \frac{15}{4})

Vereinfache

f (- \frac{3}{2} - \frac{15}{4}) : - \frac{21}{4} f

= - \frac{21}{4} f

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x \to 0 lim (\frac{x - 32}{x - 4})