integral of xsqrt(4-x^2)-x^2

Lösung

\int x 4 - x^{2} - x^{2} d x

- \frac{1}{3} (4 - x^{2})^{\frac{3}{2}} - \frac{x ^{3}}{3} + C

Schritte zur Lösung

\int x 4 - x^{2} - x^{2} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x 4 - x^{2} d x - \int x^{2} d x

\int x 4 - x^{2} d x = - \frac{1}{3} (4 - x^{2})^{\frac{3}{2}}

\int x^{2} d x = \frac{x ^{3}}{3}

= - \frac{1}{3} (4 - x^{2})^{\frac{3}{2}} - \frac{x ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{3} (4 - x^{2})^{\frac{3}{2}} - \frac{x ^{3}}{3} + C

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