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Beliebt Rechnen >

integral from 0 to x of x^3y^2

Lösung

\int_{0}^{x} x^{3} y^{2} d y

Lösung

\frac{x ^{6}}{3}

Schritte zur Lösung

\int_{0}^{x} x^{3} y^{2} d y

Entferne die Konstante:

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

= x^{3} \cdot \int_{0}^{x} y^{2} d y

Wende die Potenzregel an

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

Berechne die Grenzen:

\frac{x ^{3}}{3}

= x^{3} \frac{x ^{3}}{3}

Vereinfache

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

Beliebte Beispiele

integral from-2 to 0 of 2x+4

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

integral from 1/4 to 1/2 of 2/5 (x+2)

\int_{\frac{1}{4}}^{\frac{1}{2}} \frac{2}{5} (x + 2) d x

integral from 2 to 4 of 3xln(x)

\int_{2}^{4} 3 x ln (x) d x

integral from y to 8-y^2 of 1

\int_{y}^{8 - y^{2}} 1 d x

integral from 2 to 3 of x/8

\int_{2}^{3} \frac{x}{8} d x