integral from 0 to 10 of-x^2+10x

Lösung

\int_{0}^{10} - x^{2} + 10 x d x

\frac{500}{3}

Dezimale

166.66666 \dots

Schritte zur Lösung

\int_{0}^{10} - x^{2} + 10 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_{0}^{10} x^{2} d x + \int_{0}^{10} 10 x d x

\int_{0}^{10} x^{2} d x = \frac{1000}{3}

\int_{0}^{10} 10 x d x = 500

= - \frac{1000}{3} + 500

Vereinfache

- \frac{1000}{3} + 500 : \frac{500}{3}

= \frac{500}{3}

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