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Beliebt Rechnen >

integral from 0 to pi of cos(3x)cos(3x)

Lösung

\int_{0}^{π} cos (3 x) cos (3 x) d x

Lösung

\frac{π}{2}

+1

Dezimale

1.57079 \dots

Schritte zur Lösung

\int_{0}^{π} cos (3 x) cos (3 x) d x

Vereinfache

cos (3 x) cos (3 x) : cos^{2} (3 x)

= \int_{0}^{π} cos^{2} (3 x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

\int_{0}^{π} 1 d x = π

\int_{0}^{π} cos (6 x) d x = 0

= \frac{1}{2} (π + 0)

Vereinfache

\frac{1}{2} (π + 0) : \frac{π}{2}

= \frac{π}{2}

Graph

Beliebte Beispiele

integral of 2/(t^2-1)

\int \frac{2}{t ^{2} - 1} d t

integral of (-2)/(x^2-25)

\int \frac{- 2}{x ^{2} - 25} d x

integral of sin(x)sqrt(2+3cos(x))

\int sin (x) 2 + 3 cos (x) d x

derivative y=(3x^2+2)(2x-5)

d er i v a t i v e y = (3 x^{2} + 2) (2 x - 5)

derivative f(x)=(36)/((1+3x)^3)

d er i v a t i v e f (x) = \frac{36}{( 1 + 3 x ) ^{3}}