integral from 0 to 1 of 2pix(6-6x)

Lösung

\int_{0}^{1} 2 π x (6 - 6 x) d x

2 π

Dezimale

6.28318 \dots

Schritte zur Lösung

\int_{0}^{1} 2 π x (6 - 6 x) d x

Entferne die Konstante:

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

= 2 π \cdot \int_{0}^{1} x (6 - 6 x) d x

Wende die partielle Integration an

= 2 π [3 x^{2} (- x + 1) - \int - 3 x^{2} d x]_{0}^{1}

\int - 3 x^{2} d x = - x^{3}

= 2 π [3 x^{2} (- x + 1) - (- x^{3})]_{0}^{1}

Vereinfache

2 π [3 x^{2} (- x + 1) - (- x^{3})]_{0}^{1} : 2 π [- 2 x^{3} + 3 x^{2}]_{0}^{1}

= 2 π [- 2 x^{3} + 3 x^{2}]_{0}^{1}

Berechne die Grenzen:

1

= 2 π 1

Vereinfache

= 2 π

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