integral from 0 to 2 of cos^2(x)

Lösung

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

1 + \frac{1}{4} sin (4)

Dezimale

0.81079 \dots

Schritte zur Lösung

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{0}^{2} \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

= \frac{1}{2} \cdot \int_{0}^{2} 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

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

\int_{0}^{2} 1 d x = 2

\int_{0}^{2} cos (2 x) d x = \frac{1}{2} sin (4)

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

Vereinfache

\frac{1}{2} (2 + \frac{1}{2} sin (4)) : 1 + \frac{1}{4} sin (4)

= 1 + \frac{1}{4} sin (4)

\int_{0}^{1} \frac{1}{2 y + 1} d y

\int_{- 1}^{1} \frac{x}{1 + x ^{2}} d x

\int_{0}^{π} sin (3 x) sin (n x) d x

\int_{7}^{9} ∣ f (4 x) ∣ d x

\int_{0}^{0.5} \frac{1}{( 1 - x ) ^{2}} d x