integral from 0 to 2 of (3x-1)^{54}

Lösung

\int_{0}^{2} (3 x - 1)^{54} d x

\frac{5 ^{55} + 1}{165}

Dezimale

1.68216 E 36

Schritte zur Lösung

\int_{0}^{2} (3 x - 1)^{54} d x

Wende U-Substitution an

= \int_{- 1}^{5} \frac{u ^{54}}{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_{- 1}^{5} u^{54} d u

Wende die Potenzregel an

= \frac{1}{3} [\frac{u ^{55}}{55}]_{- 1}^{5}

Berechne die Grenzen:

\frac{5 ^{54}}{11} + \frac{1}{55}

= \frac{1}{3} (\frac{5 ^{54}}{11} + \frac{1}{55})

Vereinfache

= \frac{5 ^{55} + 1}{165}

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