integral from 0 to 2 of x 1/2 x

Lösung

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

\frac{4}{3}

Dezimale

1.33333 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{2} xx d x

Vereinfache

xx : x^{2}

= \frac{1}{2} \cdot \int_{0}^{2} x^{2} d x

Wende die Potenzregel an

= \frac{1}{2} [\frac{x ^{3}}{3}]_{0}^{2}

Berechne die Grenzen:

\frac{8}{3}

= \frac{1}{2} \cdot \frac{8}{3}

Vereinfache

= \frac{4}{3}

\int_{- 5}^{5} (2 x + 10) d x

\int_{1}^{16} \frac{5}{x} d x

\int_{- \frac{a}{2}}^{\frac{a}{2}} 1 d x

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

\int_{- 1}^{1} x^{3} - x^{5} d x