integral from 0 to 1 of x(3x^2-1)^5

Lösung

\int_{0}^{1} x (3 x^{2} - 1)^{5} d x

\frac{7}{4}

Dezimale

1.75

Schritte zur Lösung

\int_{0}^{1} x (3 x^{2} - 1)^{5} d x

Wende U-Substitution an

= \int_{- 1}^{2} \frac{u ^{5}}{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}^{2} u^{5} d u

Wende die Potenzregel an

= \frac{1}{6} [\frac{u ^{6}}{6}]_{- 1}^{2}

Berechne die Grenzen:

\frac{21}{2}

= \frac{1}{6} \cdot \frac{21}{2}

Vereinfache

= \frac{7}{4}

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