integral from 1 to 0 of |2x-1|

Lösung

\int_{1}^{0} ∣ 2 x - 1 ∣ d x

- \frac{1}{2}

Dezimale

- 0.5

Schritte zur Lösung

\int_{1}^{0} ∣ 2 x - 1 ∣ d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{1} ∣ 2 x - 1 ∣ d x

Entferne die Extremwerte

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

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

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

= - (\frac{1}{4} + \frac{1}{4})

Vereinfache

- (\frac{1}{4} + \frac{1}{4}) : - \frac{1}{2}

= - \frac{1}{2}

\int_{0}^{2} 3 x^{2} x^{3} + 1 d x

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