integral from 0 to sqrt(2 of) pi/4 z^2

Lösung

\int_{0}^{2} \frac{π}{4} z^{2} d z

\frac{π}{3 2}

Dezimale

0.74048 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{π}{4} z^{2} d z

Entferne die Konstante:

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

= \frac{π}{4} \cdot \int_{0}^{2} z^{2} d z

Wende die Potenzregel an

= \frac{π}{4} [\frac{z ^{3}}{3}]_{0}^{2}

Berechne die Grenzen:

\frac{2 2}{3}

= \frac{π}{4} \cdot \frac{2 2}{3}

Vereinfache

= \frac{π}{3 2}

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