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Beliebt Rechnen >

integral from-1 to 1 of 3x^2(2x^3+1)^2

Lösung

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

Lösung

\frac{14}{3}

+1

Dezimale

4.66666 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

= 3 \cdot \int_{- 1}^{1} x^{2} (2 x^{3} + 1)^{2} d x

Multipliziere aus

x^{2} (2 x^{3} + 1)^{2} : 4 x^{8} + 4 x^{5} + x^{2}

= 3 \cdot \int_{- 1}^{1} 4 x^{8} + 4 x^{5} + 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

= 3 (\int_{- 1}^{1} 4 x^{8} d x + \int_{- 1}^{1} 4 x^{5} d x + \int_{- 1}^{1} x^{2} d x)

\int_{- 1}^{1} 4 x^{8} d x = \frac{8}{9}

\int_{- 1}^{1} 4 x^{5} d x = 0

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

= 3 (\frac{8}{9} + 0 + \frac{2}{3})

Vereinfache

3 (\frac{8}{9} + 0 + \frac{2}{3}) : \frac{14}{3}

= \frac{14}{3}

Graph

Beliebte Beispiele

limit as x approaches 0+of (x^2-3x+2)/(x^3-2x^2)

x \to 0 + lim (\frac{x ^{2} - 3 x + 2}{x ^{3} - 2 x ^{2}})

x^2((dy)/(dx))+xy=1

x^{2} (\frac{d y}{d x}) + x y = 1

limit as x approaches 0 of (e^{x^2}-1)/x

x \to 0 lim (\frac{e ^{x^{2}} - 1}{x})

derivative (sqrt(x))/(x^3+1)

d er i v a t i v e \frac{x}{x ^{3} + 1}

(dy)/(dx)=3xcos(x^2)

\frac{d y}{d x} = 3 x cos (x^{2})