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Beliebt Rechnen >

fläche 7x+y^2=15,x=2y

Lösung

fläche

7 x + y^{2} = 15, x = 2 y

Lösung

\frac{2048}{21}

+1

Dezimale

97.52380 \dots

Schritte zur Lösung

Stelle

y

nach

7 x + y^{2} = 15

um:

y = 15 - 7 x, y = - 15 - 7 x

Stelle

y

nach

x = 2 y

um:

y = \frac{x}{2}

f_{1} (x) = 15 - 7 x

f_{2} (x) = - 15 - 7 x

Um die Schnittpunkte zu finden, löse

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

15 - 7 x = - 15 - 7 x : x = \frac{15}{7}

15 - 7 x = \frac{x}{2} : x = 2

- 15 - 7 x = \frac{x}{2} : x = - 30

= \int_{- 30}^{2} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{2}^{\frac{15}{7}} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{- 30}^{2} - 15 - 7 x - \frac{x}{2} d x + \int_{2}^{\frac{15}{7}} 15 - 7 x - (- 15 - 7 x) d x

\int_{- 30}^{2} - 15 - 7 x - \frac{x}{2} d x = \frac{292}{3}

\int_{2}^{\frac{15}{7}} 15 - 7 x - (- 15 - 7 x) d x = \frac{4}{21}

= \frac{292}{3} + \frac{4}{21}

Vereinfache

= \frac{2048}{21}

Graph

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