integral from 0 to x of (x^2)/9

Lösung

\int_{0}^{x} \frac{x ^{2}}{9} d x

\frac{x ^{3}}{27}

Schritte zur Lösung

\int_{0}^{x} \frac{x ^{2}}{9} d x

Entferne die Konstante:

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

= \frac{1}{9} \cdot \int_{0}^{x} x^{2} d x

Wende die Potenzregel an

= \frac{1}{9} [\frac{x ^{3}}{3}]_{0}^{x}

Berechne die Grenzen:

\frac{x ^{3}}{3}

= \frac{1}{9} \cdot \frac{x ^{3}}{3}

Vereinfache

= \frac{x ^{3}}{27}

\int_{1}^{e} \frac{9}{x} d x

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

\int_{0}^{7} \frac{3}{x + 9} d x

\int_{0}^{\frac{π}{2}} (cos (x) - 1) d x

\int_{- 1}^{1} (\frac{x ^{3} - 8}{x - 2}) d x