integral from 0 to pi of sin(nx)sin(x)

Lösung

\int_{0}^{π} sin (n x) sin (x) d x

0

Schritte zur Lösung

\int_{0}^{π} sin (n x) sin (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{0}^{π} \frac{- cos ( n x + x ) + cos ( n x - 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}^{π} - cos (n x + x) + cos (n x - 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}^{π} cos (n x + x) d x + \int_{0}^{π} cos (n x - x) d x)

\int_{0}^{π} cos (n x + x) d x = 0

\int_{0}^{π} cos (n x - x) d x = 0

= \frac{1}{2} (- 0 + 0)

Vereinfache

= 0

\int_{0}^{9} ∣ x - 6 ∣ d x

\int_{0}^{\frac{π}{4}} sec (t) tan (t) d t

\int_{- 2}^{0} 2 x x^{2} + 9 d x

\int_{- 2}^{0} (2 + x^{2}) d x

\int_{0}^{h} y^{2} d y