integral from 2 to y/2 of 6x^2y

Lösung

\int_{2}^{\frac{y}{2}} 6 x^{2} y d x

6 y (\frac{y ^{3}}{24} - \frac{8}{3})

Schritte zur Lösung

\int_{2}^{\frac{y}{2}} 6 x^{2} y d x

Entferne die Konstante:

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

= 6 y \cdot \int_{2}^{\frac{y}{2}} x^{2} d x

Wende die Potenzregel an

= 6 y [\frac{x ^{3}}{3}]_{2}^{\frac{y}{2}}

Berechne die Grenzen:

\frac{y ^{3}}{24} - \frac{8}{3}

= 6 y (\frac{y ^{3}}{24} - \frac{8}{3})

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