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

Lösung

\int_{0}^{2 π} ∣ sin (x) cos (x) ∣ d x

2

Schritte zur Lösung

\int_{0}^{2 π} ∣ sin (x) cos (x) ∣ d x

Entferne die Extremwerte

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

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

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

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

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

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

Vereinfache

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

= 2

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