integral from 0 to L of cos^2((pix)/(2L))

Lösung

\int_{0}^{L} cos^{2} (\frac{π x}{2 L}) d x

\frac{1}{2} L

Schritte zur Lösung

\int_{0}^{L} cos^{2} (\frac{π x}{2 L}) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{0}^{L} 1 + cos (\frac{π x}{L}) 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

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

\int_{0}^{L} 1 d x = L

\int_{0}^{L} cos (\frac{π x}{L}) d x = 0

= \frac{1}{2} (L + 0)

Vereinfache

= \frac{1}{2} L

\int_{1}^{A} \frac{1}{x} d x

\int_{0}^{\frac{7}{5}} \frac{1}{25 x ^{2} + 49} d x

\int_{0}^{π} x (7 + sin (x)) d x

\int_{0}^{1} (4 x + 1)^{2} d x

\int_{- 1}^{10} ln (x^{2} + 4 x + 12) d x