fläche x=9y^3,x=23y^2

Lösung

fläche

x = 9 y^{3}, x = 23 y^{2}

\frac{279841}{8748}

Dezimale

31.98914 \dots

Schritte zur Lösung

Stelle

y

nach

x = 9 y^{3}

um:

y = 3 \frac{x}{9}

Stelle

y

nach

x = 23 y^{2}

um:

y = \frac{x}{23}, y = - \frac{x}{23}

f_{1} (x) = 3 \frac{x}{9}

f_{2} (x) = \frac{x}{23}

Um die Schnittpunkte zu finden, löse

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

3 \frac{x}{9} = \frac{x}{23} : x = 0, x = \frac{12167}{81}

3 \frac{x}{9} = - \frac{x}{23} : x = 0

\frac{x}{23} = - \frac{x}{23} : x = 0

= \int_{0}^{\frac{12167}{81}} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{0}^{\frac{12167}{81}} 3 \frac{x}{9} - \frac{x}{23} d x

\int_{0}^{\frac{12167}{81}} 3 \frac{x}{9} - \frac{x}{23} d x = \frac{279841}{8748}

= \frac{279841}{8748}

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