integral from-2 to 5 of (x^2-3x-10)

Lösung

\int_{- 2}^{5} (x^{2} - 3 x - 10) d x

- \frac{343}{6}

Dezimale

- 57.16666 \dots

Schritte zur Lösung

\int_{- 2}^{5} x^{2} - 3 x - 10 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_{- 2}^{5} x^{2} d x - \int_{- 2}^{5} 3 x d x - \int_{- 2}^{5} 10 d x

\int_{- 2}^{5} x^{2} d x = \frac{133}{3}

\int_{- 2}^{5} 3 x d x = \frac{63}{2}

\int_{- 2}^{5} 10 d x = 70

= \frac{133}{3} - \frac{63}{2} - 70

Vereinfache

\frac{133}{3} - \frac{63}{2} - 70 : - \frac{343}{6}

= - \frac{343}{6}

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