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Beliebt Rechnen >

fläche x=y^2-10,x=3y

Lösung

fläche

x = y^{2} - 10, x = 3 y

Lösung

\frac{343}{6}

+1

Dezimale

57.16666 \dots

Schritte zur Lösung

Stelle

y

nach

x = y^{2} - 10

um:

y = x + 10, y = - x + 10

Stelle

y

nach

x = 3 y

um:

y = \frac{x}{3}

f_{1} (x) = x + 10

f_{2} (x) = - x + 10

Um die Schnittpunkte zu finden, löse

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

x + 10 = - x + 10 : x = - 10

x + 10 = \frac{x}{3} : x = 15

- x + 10 = \frac{x}{3} : x = - 6

= \int_{- 10}^{- 6} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{- 6}^{15} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 10}^{- 6} x + 10 - (- x + 10) d x + \int_{- 6}^{15} x + 10 - \frac{x}{3} d x

\int_{- 10}^{- 6} x + 10 - (- x + 10) d x = \frac{32}{3}

\int_{- 6}^{15} x + 10 - \frac{x}{3} d x = \frac{93}{2}

= \frac{32}{3} + \frac{93}{2}

Vereinfache

= \frac{343}{6}

Graph

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