integral from 0 to 2pi of |cos(2x)|

Lösung

\int_{0}^{2 π} ∣ cos (2 x) ∣ d x

4

Schritte zur Lösung

\int_{0}^{2 π} ∣ cos (2 x) ∣ d x

Entferne die Extremwerte

= \int_{0}^{\frac{π}{4}} cos (2 x) d x + \int_{\frac{π}{4}}^{\frac{3 π}{4}} - cos (2 x) d x + \int_{\frac{3 π}{4}}^{\frac{5 π}{4}} cos (2 x) d x + \int_{\frac{5 π}{4}}^{\frac{7 π}{4}} - cos (2 x) d x + \int_{\frac{7 π}{4}}^{2 π} cos (2 x) d x

\int_{0}^{\frac{π}{4}} cos (2 x) d x = \frac{1}{2}

\int_{\frac{π}{4}}^{\frac{3 π}{4}} - cos (2 x) d x = 1

\int_{\frac{3 π}{4}}^{\frac{5 π}{4}} cos (2 x) d x = 1

\int_{\frac{5 π}{4}}^{\frac{7 π}{4}} - cos (2 x) d x = 1

\int_{\frac{7 π}{4}}^{2 π} cos (2 x) d x = \frac{1}{2}

= \frac{1}{2} + 1 + 1 + 1 + \frac{1}{2}

Vereinfache

\frac{1}{2} + 1 + 1 + 1 + \frac{1}{2} : 4

= 4

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