integral from 0 to 1 of (2x-1)^6

Lösung

\int_{0}^{1} (2 x - 1)^{6} d x

\frac{1}{7}

Dezimale

0.14285 \dots

Schritte zur Lösung

\int_{0}^{1} (2 x - 1)^{6} d x

Wende U-Substitution an

= \int_{- 1}^{1} \frac{u ^{6}}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{- 1}^{1} u^{6} d u

Wende die Potenzregel an

= \frac{1}{2} [\frac{u ^{7}}{7}]_{- 1}^{1}

Berechne die Grenzen:

\frac{2}{7}

= \frac{1}{2} \cdot \frac{2}{7}

Vereinfache

= \frac{1}{7}

\int \frac{1}{( 5 x - 2 ) ^{\frac{3}{2}}} d x

x \to 2 lim (sin (x - 2) + 1)

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

d er i v a t i v e (5 x + 2) (\frac{1}{x} + 3 x^{5})

\int_{0}^{1} \frac{80}{x ^{2} - 100} d x