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Beliebt Rechnen >

fläche x=22y^2,x=5y^3

Lösung

fläche

x = 22 y^{2}, x = 5 y^{3}

Lösung

\frac{58564}{375}

+1

Dezimale

156.17066 \dots

Schritte zur Lösung

Stelle

y

nach

x = 22 y^{2}

um:

y = \frac{x}{22}, y = - \frac{x}{22}

Stelle

y

nach

x = 5 y^{3}

um:

y = 3 \frac{x}{5}

f_{1} (x) = \frac{x}{22}

f_{2} (x) = - \frac{x}{22}

Um die Schnittpunkte zu finden, löse

f_{i} (x) = f_{j} (x)

\frac{x}{22} = - \frac{x}{22} : x = 0

\frac{x}{22} = 3 \frac{x}{5} : x = 0, x = \frac{10648}{25}

- \frac{x}{22} = 3 \frac{x}{5} : x = 0

= \int_{0}^{\frac{10648}{25}} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{0}^{\frac{10648}{25}} \frac{x}{22} - 3 \frac{x}{5} d x

\int_{0}^{\frac{10648}{25}} \frac{x}{22} - 3 \frac{x}{5} d x = \frac{58564}{375}

= \frac{58564}{375}

Graph

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