integral from-5 to 1 of (x^2+4x-5)

Lösung

\int_{- 5}^{1} (x^{2} + 4 x - 5) d x

- 36

Schritte zur Lösung

\int_{- 5}^{1} x^{2} + 4 x - 5 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}^{1} x^{2} d x + \int_{- 5}^{1} 4 x d x - \int_{- 5}^{1} 5 d x

\int_{- 5}^{1} x^{2} d x = 42

\int_{- 5}^{1} 4 x d x = - 48

\int_{- 5}^{1} 5 d x = 30

= 42 - 48 - 30

Vereinfache

= - 36

\int_{0}^{1} x^{2} (x + \frac{1}{2}) d x

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