integral from-1 to 1 of x^2(x^3+1)^4

Lösung

\int_{- 1}^{1} x^{2} (x^{3} + 1)^{4} d x

\frac{32}{15}

Dezimale

2.13333 \dots

Schritte zur Lösung

\int_{- 1}^{1} x^{2} (x^{3} + 1)^{4} d x

Wende U-Substitution an

= \int_{0}^{2} \frac{u ^{4}}{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}^{2} u^{4} d u

Wende die Potenzregel an

= \frac{1}{3} [\frac{u ^{5}}{5}]_{0}^{2}

Berechne die Grenzen:

\frac{32}{5}

= \frac{1}{3} \cdot \frac{32}{5}

Vereinfache

= \frac{32}{15}

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