integral from-4 to 4 of x^2sqrt(64-x^3)

Lösung

\int_{- 4}^{4} x^{2} 64 - x^{3} d x

\frac{2048 2}{9}

Dezimale

321.81215 \dots

Schritte zur Lösung

\int_{- 4}^{4} x^{2} 64 - x^{3} d x

Wende U-Substitution an

= \int_{128}^{0} - \frac{u}{3} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{128} - \frac{u}{3} d u

Entferne die Konstante:

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

= - (- \frac{1}{3} \cdot \int_{0}^{128} u d u)

Wende die Potenzregel an

= - (- \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{128})

Vereinfache

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{128}

Berechne die Grenzen:

\frac{2048 2}{3}

= \frac{1}{3} \cdot \frac{2048 2}{3}

Vereinfache

= \frac{2048 2}{9}

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