integral from 0 to 2 of 4x^2-2x^3

Lösung

\int_{0}^{2} 4 x^{2} - 2 x^{3} d x

\frac{8}{3}

Dezimale

2.66666 \dots

Schritte zur Lösung

\int_{0}^{2} 4 x^{2} - 2 x^{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} 4 x^{2} d x - \int_{0}^{2} 2 x^{3} d x

\int_{0}^{2} 4 x^{2} d x = \frac{32}{3}

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

= \frac{32}{3} - 8

Vereinfache

\frac{32}{3} - 8 : \frac{8}{3}

= \frac{8}{3}

\frac{d}{d x} (x (x - 3)^{2})

a re a y = x^{2}, y = - x^{2} + 4 x

\int 12 sin^{6} (x) cos^{3} (x) d x

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\frac{\partial}{\partial x} (\frac{3 x + 2 y}{y ^{2} + 5 x ^{2}})