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Beliebt Rechnen >

integral from 0 to a of xsqrt(x^2+a^2)

Lösung

\int_{0}^{a} x x^{2} + a^{2} d x

Lösung

\frac{2 2 a ^{3} - a ^{3}}{3}

Schritte zur Lösung

\int_{0}^{a} x x^{2} + a^{2} d x

Wende U-Substitution an

= \int_{a^{2}}^{2 a^{2}} u^{2} d u

Wende die Potenzregel an

= [\frac{u ^{3}}{3}]_{a^{2}}^{2 a^{2}}

Vereinfache

[\frac{u ^{3}}{3}]_{a^{2}}^{2 a^{2}} : [\frac{u ^{3}}{3}]_{a}^{2 a}

= [\frac{u ^{3}}{3}]_{a}^{2 a}

Berechne die Grenzen:

\frac{2 2 a ^{3}}{3} - \frac{a ^{3}}{3}

= \frac{2 2 a ^{3}}{3} - \frac{a ^{3}}{3}

Vereinfache

= \frac{2 2 a ^{3} - a ^{3}}{3}

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