integral from-4 to 0 of x^3+x^2-6x-6x

Lösung

\int_{- 4}^{0} x^{3} + x^{2} - 6 x - 6 x d x

\frac{160}{3}

Dezimale

53.33333 \dots

Schritte zur Lösung

\int_{- 4}^{0} x^{3} + x^{2} - 6 x - 6 x d x

Vereinfache

= \int_{- 4}^{0} x^{3} + x^{2} - 12 x 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

= \int_{- 4}^{0} x^{3} d x + \int_{- 4}^{0} x^{2} d x - \int_{- 4}^{0} 12 x d x

\int_{- 4}^{0} x^{3} d x = - 64

\int_{- 4}^{0} x^{2} d x = \frac{64}{3}

\int_{- 4}^{0} 12 x d x = - 96

= - 64 + \frac{64}{3} - (- 96)

Vereinfache

- 64 + \frac{64}{3} - (- 96) : \frac{160}{3}

= \frac{160}{3}

\int_{1}^{3} x^{2} + 3 x - 4 d x

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