integral from 0 to 2pi of (θ^2)/2

Lösung

\int_{0}^{2 π} \frac{θ ^{2}}{2} d θ

\frac{4 π ^{3}}{3}

Dezimale

41.34170 \dots

Schritte zur Lösung

\int_{0}^{2 π} \frac{θ ^{2}}{2} d θ

Entferne die Konstante:

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

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

Wende die Potenzregel an

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

Berechne die Grenzen:

\frac{8 π ^{3}}{3}

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

Vereinfache

= \frac{4 π ^{3}}{3}

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