de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from-pi to pi of sin(3x)sin(3x)

Lösung

\int_{- π}^{π} sin (3 x) sin (3 x) d x

Lösung

π

+1

Dezimale

3.14159 \dots

Schritte zur Lösung

\int_{- π}^{π} sin (3 x) sin (3 x) d x

Vereinfache

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

= \int_{- π}^{π} sin^{2} (3 x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{- π}^{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_{- π}^{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_{- π}^{π} 1 d x - \int_{- π}^{π} cos (6 x) d x)

\int_{- π}^{π} 1 d x = 2 π

\int_{- π}^{π} cos (6 x) d x = 0

= \frac{1}{2} (2 π - 0)

Vereinfache

\frac{1}{2} (2 π - 0) : π

= π

Graph

Beliebte Beispiele

derivative y= 1/3 x^{3/2}

d er i v a t i v e y = \frac{1}{3} x^{\frac{3}{2}}

(\partial)/(\partial x)(2x^2+2y^2)

\frac{\partial}{\partial x} (2 x^{2} + 2 y^{2})

derivative of x/(sqrt(9-4x))

\frac{d}{d x} (\frac{x}{9 - 4 x})

y^{''}+9y=-24sin(3t)

y^{^{''}} + 9 y = - 24 sin (3 t)

(\partial)/(\partial r)(rcos(s))

\frac{\partial}{\partial r} (r cos (s))