integral from-1 to 1 of (x^2-x)/x

Lösung

\int_{- 1}^{1} \frac{x ^{2} - x}{x} d x

- 2

Schritte zur Lösung

\int_{- 1}^{1} \frac{x ^{2} - x}{x} d x

Bestimme unbestimmte (Singularitäts-)Punkte:

x = 0

Wenn

b, a < b < c, f (b) =

unbestimmt

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 1}^{0} \frac{x ^{2} - x}{x} d x + \int_{0}^{1} \frac{x ^{2} - x}{x} d x

\int_{- 1}^{0} \frac{x ^{2} - x}{x} d x = - \frac{3}{2}

\int_{0}^{1} \frac{x ^{2} - x}{x} d x = - \frac{1}{2}

= - \frac{3}{2} - \frac{1}{2}

Vereinfache

- \frac{3}{2} - \frac{1}{2} : - 2

= - 2

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