integral from 0 to 25 of pi(sqrt(x))^2

Lösung

\int_{0}^{25} π (x)^{2} d x

\frac{625 π}{2}

Dezimale

981.74770 \dots

Schritte zur Lösung

\int_{0}^{25} π (x)^{2} d x

Entferne die Konstante:

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

= π \cdot \int_{0}^{25} (x)^{2} d x

Vereinfache

(x)^{2} : x

= π \cdot \int_{0}^{25} x d x

Wende die Potenzregel an

= π [\frac{x ^{2}}{2}]_{0}^{25}

Berechne die Grenzen:

\frac{625}{2}

= π \frac{625}{2}

Vereinfache

= \frac{625 π}{2}

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