integral of cos^2(θ)

Lösung

\int cos^{2} (θ) d θ

\frac{1}{2} (θ + \frac{1}{2} sin (2 θ)) + C

Schritte zur Lösung

\int cos^{2} (θ) d θ

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int \frac{1 + cos ( 2 θ )}{2} d θ

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int 1 + cos (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

= \frac{1}{2} (\int 1 d θ + \int cos (2 θ) d θ)

\int 1 d θ = θ

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

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

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (θ + \frac{1}{2} sin (2 θ)) + C

\frac{d ^{2}}{d x ^{2}} f (x) = \frac{7}{x + 4}, at x = 0

n = 1 \sum \infty \frac{n ^{2}}{n !}

3 x^{2} e^{y} + (x^{3} e^{y} - 1) \frac{d y}{d x} = 0

t an g e n t f (x) = x sin (π x), at x = 1

t an g e n t f (x) = \frac{3}{x}, at x = \frac{1}{4}