integral from 0 to 4pi of |sin(x)|

Lösung

\int_{0}^{4 π} ∣ sin (x) ∣ d x

8

Schritte zur Lösung

\int_{0}^{4 π} ∣ sin (x) ∣ d x

Entferne die Extremwerte

= \int_{0}^{π} sin (x) d x + \int_{π}^{2 π} - sin (x) d x + \int_{2 π}^{3 π} sin (x) d x + \int_{3 π}^{4 π} - sin (x) d x

\int_{0}^{π} sin (x) d x = 2

\int_{π}^{2 π} - sin (x) d x = 2

\int_{2 π}^{3 π} sin (x) d x = 2

\int_{3 π}^{4 π} - sin (x) d x = 2

= 2 + 2 + 2 + 2

Vereinfache

= 8

\int_{0}^{2} 4 t^{2} + 1 d t

\int_{x}^{3} 1 d x

\int_{0}^{2} (2 x^{2} - 4 x) d x

\int_{2}^{8} 5 x d x

\int_{0}^{3} 12 e^{3 x} d x