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Beliebt Rechnen >

integral from 0 to r of-pir^2x

Lösung

\int_{0}^{r} - π r^{2} x d x

Lösung

- \frac{π r ^{4}}{2}

Schritte zur Lösung

\int_{0}^{r} - π r^{2} x d x

Entferne die Konstante:

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

= - π r^{2} \cdot \int_{0}^{r} x d x

Wende die Potenzregel an

= - π r^{2} [\frac{x ^{2}}{2}]_{0}^{r}

Berechne die Grenzen:

\frac{r ^{2}}{2}

= - π r^{2} \frac{r ^{2}}{2}

Vereinfache

= - \frac{π r ^{4}}{2}

Beliebte Beispiele

integral of 8x^7e^{2x^8}

\int 8 x^{7} e^{2 x^{8}} d x

derivative arccos(ax)

d er i v a t i v e arccos (a x)

(\partial)/(\partial x)(x^2+y^2+10)

\frac{\partial}{\partial x} (x^{2} + y^{2} + 10)

integral from 0 to infinity of 15e^{-5x}

\int_{0}^{\infty} 15 e^{- 5 x} d x

tangent f(x)=6x-x^2,(1,5)

t an g e n t f (x) = 6 x - x^{2}, (1, 5)