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/2 of 5cos^2(x)

Lösung

\int_{0}^{\frac{π}{2}} 5 cos^{2} (x) d x

Lösung

\frac{5 π}{4}

+1

Dezimale

3.92699 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} 5 cos^{2} (x) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int_{0}^{\frac{π}{2}} cos^{2} (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= 5 \cdot \int_{0}^{\frac{π}{2}} \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

= 5 \cdot \frac{1}{2} \cdot \int_{0}^{\frac{π}{2}} 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

= 5 \cdot \frac{1}{2} (\int_{0}^{\frac{π}{2}} 1 d x + \int_{0}^{\frac{π}{2}} cos (2 x) d x)

\int_{0}^{\frac{π}{2}} 1 d x = \frac{π}{2}

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

= 5 \cdot \frac{1}{2} (\frac{π}{2} + 0)

Vereinfache

5 \cdot \frac{1}{2} (\frac{π}{2} + 0) : \frac{5 π}{4}

= \frac{5 π}{4}

Graph

Beliebte Beispiele

y^{''}-4y^'+16y=0

y^{^{''}} - 4 y^{^{'}} + 16 y = 0

(\partial)/(\partial x)(1/(x+2ct))

\frac{\partial}{\partial x} (\frac{1}{x + 2 c t})

limit as x approaches 0 of (x+2)/(x^3+8)

x \to 0 lim (\frac{x + 2}{x ^{3} + 8})

derivative log_{3}(3x^3+4x+4)

d er i v a t i v e lo g_{3} (3 x^{3} + 4 x + 4)

integral of 7sin^6(x)cos(x)

\int 7 sin^{6} (x) cos (x) d x