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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{16 π}{3}

+1

Dezimale

16.75516 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Multipliziere aus

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

= 2 π \cdot \int_{1}^{3} - x^{3} + 4 x^{2} - 3 x 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_{1}^{3} x^{3} d x + \int_{1}^{3} 4 x^{2} d x - \int_{1}^{3} 3 x d x)

\int_{1}^{3} x^{3} d x = 20

\int_{1}^{3} 4 x^{2} d x = \frac{104}{3}

\int_{1}^{3} 3 x d x = 12

= 2 π (- 20 + \frac{104}{3} - 12)

Vereinfache

2 π (- 20 + \frac{104}{3} - 12) : \frac{16 π}{3}

= \frac{16 π}{3}

Graph

Beliebte Beispiele

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limit as x approaches-3 of x/((x+3)^4)

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y^{''}-ky=kxe^{-x}

y^{^{''}} - k y = k x e^{- x}