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Beliebt Rechnen >

integral from 0 to 2 of (2x-3)(4x^2+1)

Lösung

\int_{0}^{2} (2 x - 3) (4 x^{2} + 1) d x

Lösung

- 2

Schritte zur Lösung

\int_{0}^{2} (2 x - 3) (4 x^{2} + 1) d x

Multipliziere aus

(2 x - 3) (4 x^{2} + 1) : 8 x^{3} + 2 x - 12 x^{2} - 3

= \int_{0}^{2} 8 x^{3} + 2 x - 12 x^{2} - 3 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

= \int_{0}^{2} 8 x^{3} d x + \int_{0}^{2} 2 x d x - \int_{0}^{2} 12 x^{2} d x - \int_{0}^{2} 3 d x

\int_{0}^{2} 8 x^{3} d x = 32

\int_{0}^{2} 2 x d x = 4

\int_{0}^{2} 12 x^{2} d x = 32

\int_{0}^{2} 3 d x = 6

= 32 + 4 - 32 - 6

Vereinfache

= - 2

Graph

Beliebte Beispiele

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

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

derivative of (x^3+5e^x)

\frac{d}{d x} ((x^{3} + 5) e^{x})

integral of cos(4x)sqrt(2-sin(4x))

\int cos (4 x) 2 - sin (4 x) d x

derivative of sqrt(4(x+4^3))

\frac{d}{d x} (4 (x + 4)^{3})

tangent f(x)=x^2-3x-2,\at x=2

t an g e n t f (x) = x^{2} - 3 x - 2, at x = 2