de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 0 to pi/8 of cos^2(2x)

Lösung

\int_{0}^{\frac{π}{8}} cos^{2} (2 x) d x

Lösung

\frac{π + 2}{16}

+1

Dezimale

0.32134 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{8}} cos^{2} (2 x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{0}^{\frac{π}{8}} \frac{1}{2} (1 + cos (4 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}^{\frac{π}{8}} 1 + cos (4 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}^{\frac{π}{8}} 1 d x + \int_{0}^{\frac{π}{8}} cos (4 x) d x)

\int_{0}^{\frac{π}{8}} 1 d x = \frac{π}{8}

\int_{0}^{\frac{π}{8}} cos (4 x) d x = \frac{1}{4}

= \frac{1}{2} (\frac{π}{8} + \frac{1}{4})

Vereinfache

\frac{1}{2} (\frac{π}{8} + \frac{1}{4}) : \frac{π + 2}{16}

= \frac{π + 2}{16}

Graph

Beliebte Beispiele

taylor x^5cos(x^2)

t a y l or x^{5} cos (x^{2})

integral of sqrt(ax+b)

\int a x + b d x

derivative of in(xinx)

\frac{d}{d x} (in (x in x))

derivative of 11-x+4ln(2x-1)

\frac{d}{d x} (11 - x + 4 ln (2 x - 1))

integral of ((e^x-1)/(e^x+1))

\int (\frac{e ^{x} - 1}{e ^{x} + 1}) d x