integral from 0 to 3 of sin^2(x)

Lösung

\int_{0}^{3} sin^{2} (x) d x

\frac{1}{2} (3 - \frac{1}{2} sin (6))

Dezimale

1.56985 \dots

Schritte zur Lösung

\int_{0}^{3} sin^{2} (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{0}^{3} \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}^{3} 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}^{3} 1 d x - \int_{0}^{3} cos (2 x) d x)

\int_{0}^{3} 1 d x = 3

\int_{0}^{3} cos (2 x) d x = \frac{1}{2} sin (6)

= \frac{1}{2} (3 - \frac{1}{2} sin (6))

\int_{0}^{x} \frac{1}{x - 1} d x

\int_{- 2}^{3} x - (x^{2} - 6) d x

\int_{0}^{\infty} x e^{- k x} d x

\int_{1}^{3} x^{2} + 8 d x

\int_{x}^{1} x^{2} u^{2} + 1 d u