integral from 0 to θ of (2x^2)/(θ^2)

Lösung

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

\frac{2 θ}{3}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Potenzregel an

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

Berechne die Grenzen:

\frac{θ ^{3}}{3}

= \frac{2}{θ ^{2}} \cdot \frac{θ ^{3}}{3}

Vereinfache

= \frac{2 θ}{3}

\int_{0}^{4} π (2 x^{2})^{2} d x

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\int_{0}^{x} y x^{2} - y^{2} d y

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