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Beliebt Rechnen >

integral from-1 to 1 of 1/2 (6-6x^2)^2

Lösung

\int_{- 1}^{1} \frac{1}{2} (6 - 6 x^{2})^{2} d x

Lösung

\frac{96}{5}

+1

Dezimale

19.2

Schritte zur Lösung

\int_{- 1}^{1} \frac{1}{2} (6 - 6 x^{2})^{2} d x

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{- 1}^{1} (6 - 6 x^{2})^{2} d x

Multipliziere aus

(6 - 6 x^{2})^{2} : 36 - 72 x^{2} + 36 x^{4}

= \frac{1}{2} \cdot \int_{- 1}^{1} 36 - 72 x^{2} + 36 x^{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

= \frac{1}{2} (\int_{- 1}^{1} 36 d x - \int_{- 1}^{1} 72 x^{2} d x + \int_{- 1}^{1} 36 x^{4} d x)

\int_{- 1}^{1} 36 d x = 72

\int_{- 1}^{1} 72 x^{2} d x = 48

\int_{- 1}^{1} 36 x^{4} d x = \frac{72}{5}

= \frac{1}{2} (72 - 48 + \frac{72}{5})

Vereinfache

\frac{1}{2} (72 - 48 + \frac{72}{5}) : \frac{96}{5}

= \frac{96}{5}

Graph

Beliebte Beispiele

integral of t(t+1)^6

\int t (t + 1)^{6} d t

tangent f(x)=x^2-1,\at x=2

t an g e n t f (x) = x^{2} - 1, at x = 2

fläche y=e^x,y=e^{2x},x=0,x=ln(2)

a re a y = e^{x}, y = e^{2 x}, x = 0, x = ln (2)

tangent f(x)=4x^2-4x+1,\at x=0

t an g e n t f (x) = 4 x^{2} - 4 x + 1, at x = 0

derivative y=3x(a^2-x^2)

d er i v a t i v e y = 3 x (a^{2} - x^{2})