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Beliebt Rechnen >

fläche x+y^2=42,x+y=0

Lösung

fläche

x + y^{2} = 42, x + y = 0

Lösung

\frac{2197}{6}

+1

Dezimale

366.16666 \dots

Schritte zur Lösung

Stelle

y

nach

x + y^{2} = 42

um:

y = 42 - x, y = - 42 - x

Stelle

y

nach

x + y = 0

um:

y = - x

f_{1} (x) = 42 - x

f_{2} (x) = - 42 - x

Um die Schnittpunkte zu finden, löse

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

42 - x = - 42 - x : x = 42

42 - x = - x : x = - 7

- 42 - x = - x : x = 6

= \int_{- 7}^{6} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{6}^{42} ∣ f_{2} (x) - f_{1} (x) ∣ d x

= \int_{- 7}^{6} 42 - x - (- x) d x + \int_{6}^{42} - 42 - x - 42 - x d x

\int_{- 7}^{6} 42 - x - (- x) d x = \frac{469}{6}

\int_{6}^{42} - 42 - x - 42 - x d x = 288

= \frac{469}{6} + 288

Vereinfache

= \frac{2197}{6}

Graph

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