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 9cos^2(x)

Lösung

\int_{0}^{\frac{π}{2}} 9 cos^{2} (x) d x

Lösung

\frac{9 π}{4}

+1

Dezimale

7.06858 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} 9 cos^{2} (x) d x

Entferne die Konstante:

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

= 9 \cdot \int_{0}^{\frac{π}{2}} cos^{2} (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= 9 \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

= 9 \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

= 9 \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

= 9 \cdot \frac{1}{2} (\frac{π}{2} + 0)

Vereinfache

9 \cdot \frac{1}{2} (\frac{π}{2} + 0) : \frac{9 π}{4}

= \frac{9 π}{4}

Graph

Beliebte Beispiele

integral of 8x(4x^2+3)^6

\int 8 x (4 x^{2} + 3)^{6} d x

integral from 0 to 1 of 1/(sqrt(4-x^2))

\int_{0}^{1} \frac{1}{4 - x ^{2}} d x

fläche x=y^2-6x,x=y-y^2

a re a x = y^{2} - 6 x, x = y - y^{2}

(\partial)/(\partial x)(7e^{x-y})

\frac{\partial}{\partial x} (7 e^{x - y})

(3x^2+4xy)dx+(2x^2+2y)dy=0

(3 x^{2} + 4 x y) d x + (2 x^{2} + 2 y) d y = 0