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 1 of 2pi(x+8)(x^2)

Lösung

\int_{0}^{1} 2 π (x + 8) (x^{2}) d x

Lösung

\frac{35 π}{6}

+1

Dezimale

18.32595 \dots

Schritte zur Lösung

\int_{0}^{1} 2 π (x + 8) x^{2} d x

Entferne die Konstante:

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

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

Multipliziere aus

(x + 8) x^{2} : x^{3} + 8 x^{2}

= 2 π \cdot \int_{0}^{1} x^{3} + 8 x^{2} 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

= 2 π (\int_{0}^{1} x^{3} d x + \int_{0}^{1} 8 x^{2} d x)

\int_{0}^{1} x^{3} d x = \frac{1}{4}

\int_{0}^{1} 8 x^{2} d x = \frac{8}{3}

= 2 π (\frac{1}{4} + \frac{8}{3})

Vereinfache

2 π (\frac{1}{4} + \frac{8}{3}) : \frac{35 π}{6}

= \frac{35 π}{6}

Graph

Beliebte Beispiele

derivative (y,(x+y))/((x^2+y^2+xy+3))

d er i v a t i v e \frac{y , ( x + y )}{( x ^{2} + y ^{2} + x y + 3 )}

integral of (1+2x)e^{-x}

\int (1 + 2 x) e^{- x} d x

integral of (x^2)/(x^2-6x+25)

\int \frac{x ^{2}}{x ^{2} - 6 x + 25} d x

(\partial)/(\partial x)(x^x)

\frac{\partial}{\partial x} (x^{x})

limit as x approaches infinity of 9.35e^{(-0.4x)}+5.52

x \to \infty lim (9.35 e^{(- 0.4 x)} + 5.52)