integral from 0 to 8 of |x^2-6x+5|

Lösung

\int_{0}^{8} x^{2} - 6 x + 5 d x

40

Schritte zur Lösung

\int_{0}^{8} x^{2} - 6 x + 5 d x

Entferne die Extremwerte

= \int_{0}^{1} x^{2} - 6 x + 5 d x + \int_{1}^{5} - x^{2} + 6 x - 5 d x + \int_{5}^{8} x^{2} - 6 x + 5 d x

\int_{0}^{1} x^{2} - 6 x + 5 d x = \frac{7}{3}

\int_{1}^{5} - x^{2} + 6 x - 5 d x = \frac{32}{3}

\int_{5}^{8} x^{2} - 6 x + 5 d x = 27

= \frac{7}{3} + \frac{32}{3} + 27

Vereinfache

\frac{7}{3} + \frac{32}{3} + 27 : 40

= 40

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