integral from 0 to 2 of (6x-6)(4x^2+5)

Lösung

\int_{0}^{2} (6 x - 6) (4 x^{2} + 5) d x

32

Schritte zur Lösung

\int_{0}^{2} (6 x - 6) (4 x^{2} + 5) d x

Wende die partielle Integration an

= [(4 x^{2} + 5) (3 x^{2} - 6 x) - \int 8 x (3 x^{2} - 6 x) d x]_{0}^{2}

\int 8 x (3 x^{2} - 6 x) d x = 8 (\frac{3 x ^{4}}{4} - 2 x^{3})

= [(4 x^{2} + 5) (3 x^{2} - 6 x) - 8 (\frac{3 x ^{4}}{4} - 2 x^{3})]_{0}^{2}

Multipliziere aus

(4 x^{2} + 5) (3 x^{2} - 6 x) - 8 (\frac{3 x ^{4}}{4} - 2 x^{3}) : 6 x^{4} - 8 x^{3} + 15 x^{2} - 30 x

= [6 x^{4} - 8 x^{3} + 15 x^{2} - 30 x]_{0}^{2}

Berechne die Grenzen:

32

= 32

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