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

Lösung

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

\frac{5}{4}

Dezimale

1.25

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{- 1}^{2} \frac{u ^{3}}{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^{3} d u

Wende die Potenzregel an

= \frac{1}{3} [\frac{u ^{4}}{4}]_{- 1}^{2}

Berechne die Grenzen:

\frac{15}{4}

= \frac{1}{3} \cdot \frac{15}{4}

Vereinfache

= \frac{5}{4}

\int_{0}^{\frac{π}{4}} e^{x} sin (e^{x}) d x

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

\int_{1}^{2} (x + e^{- y}) d x

\int_{10}^{7} g (x) d x

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