integral from-2 to 0 of (3t^3-t^2-9t-1)

Lösung

\int_{- 2}^{0} (3 t^{3} - t^{2} - 9 t - 1) d t

\frac{4}{3}

Dezimale

1.33333 \dots

Schritte zur Lösung

\int_{- 2}^{0} 3 t^{3} - t^{2} - 9 t - 1 d t

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 2}^{0} 3 t^{3} d t - \int_{- 2}^{0} t^{2} d t - \int_{- 2}^{0} 9 t d t - \int_{- 2}^{0} 1 d t

\int_{- 2}^{0} 3 t^{3} d t = - 12

\int_{- 2}^{0} t^{2} d t = \frac{8}{3}

\int_{- 2}^{0} 9 t d t = - 18

\int_{- 2}^{0} 1 d t = 2

= - 12 - \frac{8}{3} - (- 18) - 2

Vereinfache

- 12 - \frac{8}{3} - (- 18) - 2 : \frac{4}{3}

= \frac{4}{3}

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