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Beliebt Rechnen >

integral from-6 to 0 of ([ 1/2 x]+|x|)

Lösung

\int_{- 6}^{0} ([\frac{1}{2} x] + ∣ x ∣) d x

Lösung

9

Schritte zur Lösung

\int_{- 6}^{0} [\frac{1}{2} x] + ∣ x ∣ d x

Entferne die Extremwerte

= \int_{- 6}^{0} [\frac{1}{2} x] - 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_{- 6}^{0} \frac{1}{2} x d x - \int_{- 6}^{0} x d x

\int_{- 6}^{0} \frac{1}{2} x d x = - 9

\int_{- 6}^{0} x d x = - 18

= - 9 - (- 18)

Vereinfache

= 9

Graph

Beliebte Beispiele

integral from-1 to 3 of |x|-1

\int_{- 1}^{3} ∣ x ∣ - 1 d x

integral from 1 to 3 of 1/(x^4)

\int_{1}^{3} \frac{1}{x ^{4}} d x

integral from 0 to 1 of sqrt(5x+6)

\int_{0}^{1} 5 x + 6 d x

integral from 1 to 4 of 2x^2

\int_{1}^{4} 2 x^{2} d x

integral from 0 to 8 of 8x

\int_{0}^{8} 8 x d x