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Beliebt Rechnen >

integral of (4-r^2)r

Lösung

\int (4 - r^{2}) r d r

Lösung

2 r^{2} - \frac{r ^{4}}{4} + C

Schritte zur Lösung

\int (4 - r^{2}) r d r

Multipliziere aus

(4 - r^{2}) r : 4 r - r^{3}

= \int 4 r - r^{3} d r

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 r d r - \int r^{3} d r

\int 4 r d r = 2 r^{2}

\int r^{3} d r = \frac{r ^{4}}{4}

= 2 r^{2} - \frac{r ^{4}}{4}

Füge eine Konstante zur Lösung hinzu

= 2 r^{2} - \frac{r ^{4}}{4} + C

Graph

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