integral from 0 to 5 of |x^2-4x+3|

Lösung

\int_{0}^{5} x^{2} - 4 x + 3 d x

\frac{28}{3}

Dezimale

9.33333 \dots

Schritte zur Lösung

\int_{0}^{5} x^{2} - 4 x + 3 d x

Entferne die Extremwerte

= \int_{0}^{1} x^{2} - 4 x + 3 d x + \int_{1}^{3} - x^{2} + 4 x - 3 d x + \int_{3}^{5} x^{2} - 4 x + 3 d x

\int_{0}^{1} x^{2} - 4 x + 3 d x = \frac{4}{3}

\int_{1}^{3} - x^{2} + 4 x - 3 d x = \frac{4}{3}

\int_{3}^{5} x^{2} - 4 x + 3 d x = \frac{20}{3}

= \frac{4}{3} + \frac{4}{3} + \frac{20}{3}

Vereinfache

\frac{4}{3} + \frac{4}{3} + \frac{20}{3} : \frac{28}{3}

= \frac{28}{3}

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