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Beliebt Rechnen >

integral from 0 to 2 of-6x^3sqrt(x^2+4)

Lösung

\int_{0}^{2} - 6 x^{3} x^{2} + 4 d x

Lösung

- \frac{2 ( 64 2 + 64 )}{5}

+1

Dezimale

- 61.80386 \dots

Schritte zur Lösung

\int_{0}^{2} - 6 x^{3} x^{2} + 4 d x

Entferne die Konstante:

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

= - 6 \cdot \int_{0}^{2} x^{3} x^{2} + 4 d x

Wende U-Substitution an

= - 6 \cdot \int_{2}^{22} (u^{2} - 4) u^{2} d u

Multipliziere aus

(u^{2} - 4) u^{2} : u^{4} - 4 u^{2}

= - 6 \cdot \int_{2}^{22} u^{4} - 4 u^{2} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - 6 (\int_{2}^{22} u^{4} d u - \int_{2}^{22} 4 u^{2} d u)

\int_{2}^{22} u^{4} d u = \frac{128 2 - 32}{5}

\int_{2}^{22} 4 u^{2} d u = \frac{4 ( 16 2 - 8 )}{3}

= - 6 (\frac{128 2 - 32}{5} - \frac{4 ( 16 2 - 8 )}{3})

Vereinfache

- 6 (\frac{128 2 - 32}{5} - \frac{4 ( 16 2 - 8 )}{3}) : - \frac{2 ( 64 2 + 64 )}{5}

= - \frac{2 ( 64 2 + 64 )}{5}

Graph

Beliebte Beispiele

derivative of 1+x+5x^2

\frac{d}{d x} (1 + x + 5 x^{2})

integral from-2 to 1 of 2-x^2-x

\int_{- 2}^{1} 2 - x^{2} - x d x

derivative (x^9-1)^3

d er i v a t i v e (x^{9} - 1)^{3}

derivative (x^2-6x+1)/(x^2+7)

d er i v a t i v e \frac{x ^{2} - 6 x + 1}{x ^{2} + 7}

derivative of 1/2 e^{x/2}

\frac{d}{d x} (\frac{1}{2} e^{\frac{x}{2}})