integral from 0 to 1 of (2x-1)^{100}

Lösung

\int_{0}^{1} (2 x - 1)^{100} d x

\frac{1}{101}

Dezimale

0.00990 \dots

Schritte zur Lösung

\int_{0}^{1} (2 x - 1)^{100} d x

Wende U-Substitution an

= \int_{- 1}^{1} \frac{u ^{100}}{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^{100} d u

Wende die Potenzregel an

= \frac{1}{2} [\frac{u ^{101}}{101}]_{- 1}^{1}

Berechne die Grenzen:

\frac{2}{101}

= \frac{1}{2} \cdot \frac{2}{101}

Vereinfache

= \frac{1}{101}

\int_{0}^{x} \frac{6 x}{( 1 + x ) ^{4}} d x

\int_{0}^{1} 2^{x} + x d x

\int_{0}^{1} \frac{1}{x ^{4} + 1} d x

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

\int_{0}^{4} (x^{2} - 2 y^{2}) d x