integral from 1 to 8 of (x^2-4x-12)

Lösung

\int_{1}^{8} (x^{2} - 4 x - 12) d x

- \frac{119}{3}

Dezimale

- 39.66666 \dots

Schritte zur Lösung

\int_{1}^{8} x^{2} - 4 x - 12 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}^{8} x^{2} d x - \int_{1}^{8} 4 x d x - \int_{1}^{8} 12 d x

\int_{1}^{8} x^{2} d x = \frac{511}{3}

\int_{1}^{8} 4 x d x = 126

\int_{1}^{8} 12 d x = 84

= \frac{511}{3} - 126 - 84

Vereinfache

\frac{511}{3} - 126 - 84 : - \frac{119}{3}

= - \frac{119}{3}

\int_{0}^{1} 2 x^{2} + 1 d x

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