integral from 0 to 2pi of 1-cos(2x)

Lösung

\int_{0}^{2 π} 1 - cos (2 x) d x

2 π

Dezimale

6.28318 \dots

Schritte zur Lösung

\int_{0}^{2 π} 1 - cos (2 x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{0}^{2 π} 1 d x = 2 π

\int_{0}^{2 π} cos (2 x) d x = 0

= 2 π - 0

Vereinfache

= 2 π

\int_{0}^{1} (x^{2} - 2 x + 7) d x

\int_{- 2}^{2} x^{4} - 2 x^{2} d x

\int_{0}^{1} 2 x z e^{- x^{2}} d x

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

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