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 of 1/2 sin^2(x)

Lösung

\int_{0}^{π} \frac{1}{2} sin^{2} (x) d x

Lösung

\frac{π}{4}

+1

Dezimale

0.78539 \dots

Schritte zur Lösung

\int_{0}^{π} \frac{1}{2} sin^{2} (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} sin^{2} (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

\int_{0}^{π} 1 d x = π

\int_{0}^{π} cos (2 x) d x = 0

= \frac{1}{2} \cdot \frac{1}{2} (π - 0)

Vereinfache

\frac{1}{2} \cdot \frac{1}{2} (π - 0) : \frac{π}{4}

= \frac{π}{4}

Graph

Beliebte Beispiele

integral from-1 to 3 of 4^x

\int_{- 1}^{3} 4^{x} d x

integral from 1 to 2 of x^4-x

\int_{1}^{2} x^{4} - x d x

integral from 0 to t of μe^{t-μ}

\int_{0}^{t} μ e^{t - μ} d μ

integral from 0 to 1 of 5/(4x+1)

\int_{0}^{1} \frac{5}{4 x + 1} d x

integral from 3 to 8 of x^3

\int_{3}^{8} x^{3} d x