integral from 0 to 2 of (6x-3)(4x^2+7)

Lösung

\int_{0}^{2} (6 x - 3) (4 x^{2} + 7) d x

106

Schritte zur Lösung

\int_{0}^{2} (6 x - 3) (4 x^{2} + 7) d x

Wende die partielle Integration an

= [(4 x^{2} + 7) (3 x^{2} - 3 x) - \int 8 x (3 x^{2} - 3 x) d x]_{0}^{2}

\int 8 x (3 x^{2} - 3 x) d x = 8 (\frac{3}{4} x^{4} - x^{3})

= [(4 x^{2} + 7) (3 x^{2} - 3 x) - 8 (\frac{3}{4} x^{4} - x^{3})]_{0}^{2}

Multipliziere aus

(4 x^{2} + 7) (3 x^{2} - 3 x) - 8 (\frac{3}{4} x^{4} - x^{3}) : 6 x^{4} - 4 x^{3} + 21 x^{2} - 21 x

= [6 x^{4} - 4 x^{3} + 21 x^{2} - 21 x]_{0}^{2}

Berechne die Grenzen:

106

= 106

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