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Beliebt Rechnen >

integral of sin^2((2pix)/L)

Lösung

\int sin^{2} (\frac{2 π x}{L}) d x

Lösung

\frac{1}{2} (x - \frac{1}{4 π} L sin (\frac{4 π x}{L})) + C

Schritte zur Lösung

\int sin^{2} (\frac{2 π x}{L}) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int \frac{1}{2} (1 - cos (\frac{4 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 1 - cos (\frac{4 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 1 d x - \int cos (\frac{4 π x}{L}) d x)

\int 1 d x = x

\int cos (\frac{4 π x}{L}) d x = \frac{1}{4 π} L sin (\frac{4 π x}{L})

= \frac{1}{2} (x - \frac{1}{4 π} L sin (\frac{4 π x}{L}))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (x - \frac{1}{4 π} L sin (\frac{4 π x}{L})) + C

Graph

Beliebte Beispiele

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x \to 3 lim (\frac{7 x ^{2} - 3 x}{x})

1/4 ((dy)/(dt))+10y=5

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\int sec^{2} (x t a) n^{2} x d x

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