integral from-5 to 0 of 2x-x^2-7x

Lösung

\int_{- 5}^{0} 2 x - x^{2} - 7 x d x

\frac{125}{6}

Dezimale

20.83333 \dots

Schritte zur Lösung

\int_{- 5}^{0} 2 x - x^{2} - 7 x d x

Vereinfache

= \int_{- 5}^{0} - x^{2} - 5 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_{- 5}^{0} x^{2} d x - \int_{- 5}^{0} 5 x d x

\int_{- 5}^{0} x^{2} d x = \frac{125}{3}

\int_{- 5}^{0} 5 x d x = - \frac{125}{2}

= - \frac{125}{3} - (- \frac{125}{2})

Vereinfache

- \frac{125}{3} - (- \frac{125}{2}) : \frac{125}{6}

= \frac{125}{6}

\int_{1}^{2} (3 - x) - (\frac{2}{x}) d x

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