integral from-1 to 7 of (|x-2|-3)

Lösung

\int_{- 1}^{7} (∣ x - 2 ∣ - 3) d x

- 7

Schritte zur Lösung

\int_{- 1}^{7} ∣ x - 2 ∣ - 3 d x

Entferne die Extremwerte

= \int_{- 1}^{2} - x + 2 - 3 d x + \int_{2}^{7} x - 2 - 3 d x

\int_{- 1}^{2} - x + 2 - 3 d x = - \frac{9}{2}

\int_{2}^{7} x - 2 - 3 d x = - \frac{5}{2}

= - \frac{9}{2} - \frac{5}{2}

Vereinfache

- \frac{9}{2} - \frac{5}{2} : - 7

= - 7

\int_{- 1}^{8} x^{\frac{1}{3}} d x

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