integral from 0 to 1 of (3t-1)^{50}

Lösung

\int_{0}^{1} (3 t - 1)^{50} d t

\frac{2 ^{51} + 1}{153}

Dezimale

1.47176 E 13

Schritte zur Lösung

\int_{0}^{1} (3 t - 1)^{50} d t

Wende U-Substitution an

= \int_{- 1}^{2} \frac{u ^{50}}{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}^{2} u^{50} d u

Wende die Potenzregel an

= \frac{1}{3} [\frac{u ^{51}}{51}]_{- 1}^{2}

Berechne die Grenzen:

\frac{2 ^{51}}{51} + \frac{1}{51}

= \frac{1}{3} (\frac{2 ^{51}}{51} + \frac{1}{51})

Vereinfache

= \frac{2 ^{51} + 1}{153}

x \to \infty lim (\frac{x}{4})

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