integral from 0 to 2pi of (1+sin(x))^2

Lösung

\int_{0}^{2 π} (1 + sin (x))^{2} d x

3 π

Dezimale

9.42477 \dots

Schritte zur Lösung

\int_{0}^{2 π} (1 + sin (x))^{2} d x

Multipliziere aus

(1 + sin (x))^{2} : 1 + 2 sin (x) + sin^{2} (x)

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

\int_{0}^{2 π} 1 d x = 2 π

\int_{0}^{2 π} 2 sin (x) d x = 0

\int_{0}^{2 π} sin^{2} (x) d x = π

= 2 π + 0 + π

Vereinfache

= 3 π

\int_{0}^{1 + i} z^{2} d z

\int_{- 1}^{1} e^{x} \cdot x d x

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

\int_{0}^{π} (π^{2} - x^{2}) d x

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