integral from-5 to 6 of (36-x^2)-(6-x)

Lösung

\int_{- 5}^{6} (36 - x^{2}) - (6 - x) d x

\frac{1331}{6}

Dezimale

221.83333 \dots

Schritte zur Lösung

\int_{- 5}^{6} 36 - x^{2} - (6 - x) d x

Vereinfache

= \int_{- 5}^{6} - x^{2} + x + 30 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_{- 5}^{6} x^{2} d x + \int_{- 5}^{6} x d x + \int_{- 5}^{6} 30 d x

\int_{- 5}^{6} x^{2} d x = \frac{341}{3}

\int_{- 5}^{6} x d x = \frac{11}{2}

\int_{- 5}^{6} 30 d x = 330

= - \frac{341}{3} + \frac{11}{2} + 330

Vereinfache

- \frac{341}{3} + \frac{11}{2} + 330 : \frac{1331}{6}

= \frac{1331}{6}

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