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 3cos^5(x)

Lösung

\int_{0}^{\frac{π}{2}} 3 cos^{5} (x) d x

Lösung

\frac{8}{5}

+1

Dezimale

1.6

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} 3 cos^{5} (x) d x

Entferne die Konstante:

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

= 3 \cdot \int_{0}^{\frac{π}{2}} cos^{5} (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= 3 \cdot \int_{0}^{\frac{π}{2}} (1 - sin^{2} (x))^{2} cos (x) d x

Wende U-Substitution an

= 3 \cdot \int_{0}^{1} (1 - u^{2})^{2} d u

Multipliziere aus

(1 - u^{2})^{2} : 1 - 2 u^{2} + u^{4}

= 3 \cdot \int_{0}^{1} 1 - 2 u^{2} + u^{4} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 3 (\int_{0}^{1} 1 d u - \int_{0}^{1} 2 u^{2} d u + \int_{0}^{1} u^{4} d u)

\int_{0}^{1} 1 d u = 1

\int_{0}^{1} 2 u^{2} d u = \frac{2}{3}

\int_{0}^{1} u^{4} d u = \frac{1}{5}

= 3 (1 - \frac{2}{3} + \frac{1}{5})

Vereinfache

3 (1 - \frac{2}{3} + \frac{1}{5}) : \frac{8}{5}

= \frac{8}{5}

Graph

Beliebte Beispiele

derivative of x^{1/4}-4e^x

\frac{d}{d x} (x^{\frac{1}{4}} - 4 e^{x})

inverselaplace 6/s+16(1/(s^2+16))

in v erse l a pl a ce \frac{6}{s} + 16 (\frac{1}{s ^{2} + 16})

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

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

derivative of cos(x+2sin(x))

\frac{d}{d x} (cos (x) + 2 sin (x))

integral of (-2x)/(x^2-1)

\int \frac{- 2 x}{x ^{2} - 1} d x