integral from 0 to x of ysqrt(x^2-y^2)

Lösung

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

\frac{( x ^{2} ) ^{\frac{3}{2}}}{3}

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{x^{2}}^{0} - \frac{u}{2} d u

Entferne die Konstante:

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

= - \frac{1}{2} \cdot \int_{x^{2}}^{0} u d u

Wende die Potenzregel an

= - \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{x^{2}}^{0}

Berechne die Grenzen:

- \frac{2}{3} (x^{2})^{\frac{3}{2}}

= - \frac{1}{2} (- \frac{2}{3} (x^{2})^{\frac{3}{2}})

Vereinfache

= \frac{( x ^{2} ) ^{\frac{3}{2}}}{3}

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