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Beliebt Rechnen >

integral from-2pi to 2pi of pisin^2(x)

Lösung

\int_{- 2 π}^{2 π} π sin^{2} (x) d x

Lösung

2 π^{2}

+1

Dezimale

19.73920 \dots

Schritte zur Lösung

\int_{- 2 π}^{2 π} π sin^{2} (x) d x

Entferne die Konstante:

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

= π \cdot \int_{- 2 π}^{2 π} sin^{2} (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

Entferne die Konstante:

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

= π \frac{1}{2} \cdot \int_{- 2 π}^{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

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

\int_{- 2 π}^{2 π} 1 d x = 4 π

\int_{- 2 π}^{2 π} cos (2 x) d x = 0

= π \frac{1}{2} (4 π - 0)

Vereinfache

π \frac{1}{2} (4 π - 0) : 2 π^{2}

= 2 π^{2}

Graph

Beliebte Beispiele

integral of sec^3(1-4x)

\int sec^{3} (1 - 4 x) d x

y^{''}-10y^'+25y=0,y(0)=0,y^'(0)=3

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 0, y^{^{'}} (0) = 3

integral of xe^{-2x}

\int x e^{- 2 x} d x

integral of (x^2)/(x-7)

\int \frac{x ^{2}}{x - 7} d x

derivative of 1/(x^4-3/(x^2))

\frac{d}{d x} (\frac{1}{x ^{4}} - \frac{3}{x ^{2}})