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 2 of 2pix(3+(x^2)/3)

Lösung

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

Lösung

\frac{44 π}{3}

+1

Dezimale

46.07669 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

= 2 π [\frac{1}{6} x^{2} (9 + x^{2}) - \int \frac{x ^{3}}{3} d x]_{0}^{2}

\int \frac{x ^{3}}{3} d x = \frac{x ^{4}}{12}

= 2 π [\frac{1}{6} x^{2} (9 + x^{2}) - \frac{x ^{4}}{12}]_{0}^{2}

Vereinfache

2 π [\frac{1}{6} x^{2} (9 + x^{2}) - \frac{x ^{4}}{12}]_{0}^{2} : 2 π [\frac{1}{12} (18 x^{2} + x^{4})]_{0}^{2}

= 2 π [\frac{1}{12} (18 x^{2} + x^{4})]_{0}^{2}

Berechne die Grenzen:

\frac{22}{3}

= 2 π \frac{22}{3}

Vereinfache

= \frac{44 π}{3}

Graph

Beliebte Beispiele

f(x)=(sin(x)+cos(x))/(sin(x)-cos(x))

f (x) = \frac{sin ( x ) + cos ( x )}{sin ( x ) - cos ( x )}

(1+x^3)dy-x^2ydx=0

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

x d y + y ln (y) d x = 0

integral of (2x^5+1)/(2x-2x^5)

\int \frac{2 x ^{5} + 1}{2 x - 2 x ^{5}} d x

integral of x(x^2+1)^3

\int x (x^{2} + 1)^{3} d x