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Beliebt Rechnen >

integral of (2-sin(θ))^2

Lösung

\int (2 - sin (θ))^{2} d θ

Lösung

\frac{9}{2} θ - \frac{1}{4} sin (2 θ) + 4 cos (θ) + C

Schritte zur Lösung

\int (2 - sin (θ))^{2} d θ

Multipliziere aus

(2 - sin (θ))^{2} : 4 - 4 sin (θ) + sin^{2} (θ)

= \int 4 - 4 sin (θ) + sin^{2} (θ) d θ

Wende die Summenregel an:

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

= \int 4 d θ - \int 4 sin (θ) d θ + \int sin^{2} (θ) d θ

\int 4 d θ = 4 θ

\int 4 sin (θ) d θ = - 4 cos (θ)

\int sin^{2} (θ) d θ = \frac{1}{2} (θ - \frac{1}{2} sin (2 θ))

= 4 θ - (- 4 cos (θ)) + \frac{1}{2} (θ - \frac{1}{2} sin (2 θ))

Vereinfache

4 θ - (- 4 cos (θ)) + \frac{1}{2} (θ - \frac{1}{2} sin (2 θ)) : \frac{9}{2} θ - \frac{1}{4} sin (2 θ) + 4 cos (θ)

= \frac{9}{2} θ - \frac{1}{4} sin (2 θ) + 4 cos (θ)

Füge eine Konstante zur Lösung hinzu

= \frac{9}{2} θ - \frac{1}{4} sin (2 θ) + 4 cos (θ) + C

Graph

Beliebte Beispiele

inverselaplace 2/((s+1)^2)

in v erse l a pl a ce \frac{2}{( s + 1 ) ^{2}}

integral of 6cos^2(x)

\int 6 cos^{2} (x) d x

y^{''}+7y^'-18y=0

y^{^{''}} + 7 y^{^{'}} - 18 y = 0

derivative (x-5xsqrt(x))/(sqrt(x))

d er i v a t i v e \frac{x - 5 x x}{x}

limit as x approaches 5 of (12)/(5-x)

x \to 5 lim (\frac{12}{5 - x})