integral from 0 to y^2 of x^2y

Lösung

\int_{0}^{y^{2}} x^{2} y d x

\frac{y ^{7}}{3}

Schritte zur Lösung

\int_{0}^{y^{2}} x^{2} y d x

Entferne die Konstante:

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

= y \cdot \int_{0}^{y^{2}} x^{2} d x

Wende die Potenzregel an

= y [\frac{x ^{3}}{3}]_{0}^{y^{2}}

Berechne die Grenzen:

\frac{y ^{6}}{3}

= y \frac{y ^{6}}{3}

Vereinfache

= \frac{y ^{7}}{3}

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