integral from 0 to 2 of 2pix(1+(x^2)/4)

Lösung

\int_{0}^{2} 2 π x (1 + \frac{x ^{2}}{4}) d x

6 π

Dezimale

18.84955 \dots

Schritte zur Lösung

\int_{0}^{2} 2 π x (1 + \frac{x ^{2}}{4}) 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 (1 + \frac{x ^{2}}{4}) d x

Multipliziere aus

x (1 + \frac{x ^{2}}{4}) : x + \frac{x ^{3}}{4}

= 2 π \cdot \int_{0}^{2} x + \frac{x ^{3}}{4} 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}^{2} x d x + \int_{0}^{2} \frac{x ^{3}}{4} d x)

\int_{0}^{2} x d x = 2

\int_{0}^{2} \frac{x ^{3}}{4} d x = 1

= 2 π (2 + 1)

Vereinfache

= 6 π

\int_{y}^{x} \frac{1}{x ^{2}} d x

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

\int_{1}^{2} (1 - \frac{x}{2}) d x

\int_{- c}^{c} (c - x^{2}) - (x^{2} - c) d x

\int_{0}^{2} \frac{x ^{2}}{x ^{3} + 4} d x