integral from-1 to 4 of x^2-4x-5

Lösung

\int_{- 1}^{4} x^{2} - 4 x - 5 d x

- \frac{100}{3}

Dezimale

- 33.33333 \dots

Schritte zur Lösung

\int_{- 1}^{4} x^{2} - 4 x - 5 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_{- 1}^{4} x^{2} d x - \int_{- 1}^{4} 4 x d x - \int_{- 1}^{4} 5 d x

\int_{- 1}^{4} x^{2} d x = \frac{65}{3}

\int_{- 1}^{4} 4 x d x = 30

\int_{- 1}^{4} 5 d x = 25

= \frac{65}{3} - 30 - 25

Vereinfache

\frac{65}{3} - 30 - 25 : - \frac{100}{3}

= - \frac{100}{3}

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