integral from 0 to 1 of x^2(1+2x^3)^3

Lösung

\int_{0}^{1} x^{2} (1 + 2 x^{3})^{3} d x

\frac{10}{3}

Dezimale

3.33333 \dots

Schritte zur Lösung

\int_{0}^{1} x^{2} (1 + 2 x^{3})^{3} d x

Wende U-Substitution an

= \int_{1}^{3} \frac{u ^{3}}{6} d u

Entferne die Konstante:

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

= \frac{1}{6} \cdot \int_{1}^{3} u^{3} d u

Wende die Potenzregel an

= \frac{1}{6} [\frac{u ^{4}}{4}]_{1}^{3}

Berechne die Grenzen:

20

= \frac{1}{6} \cdot 20

Vereinfache

= \frac{10}{3}

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