integral from x to 1 of sin^2(t)

Lösung

\int_{x}^{1} sin^{2} (t) d t

\frac{1}{2} (1 - x - \frac{1}{2} (sin (2) - sin (2 x)))

Schritte zur Lösung

\int_{x}^{1} sin^{2} (t) d t

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

Entferne die Konstante:

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

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

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_{x}^{1} 1 d t - \int_{x}^{1} cos (2 t) d t)

\int_{x}^{1} 1 d t = 1 - x

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

= \frac{1}{2} (1 - x - \frac{1}{2} (sin (2) - sin (2 x)))

\int_{- 1}^{1} t^{3} d t

\int_{0}^{2} t 1 + 4 t^{2} d t

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

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

\int_{0}^{2 π} sin (y) d y