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Beliebt Rechnen >

fläche y^2-7x=1,x-y=1

Lösung

fläche

y^{2} - 7 x = 1, x - y = 1

Lösung

\frac{243}{14}

+1

Dezimale

17.35714 \dots

Schritte zur Lösung

Stelle

y

nach

y^{2} - 7 x = 1

um:

y = 1 + 7 x, y = - 1 + 7 x

Stelle

y

nach

x - y = 1

um:

y = - 1 + x

f_{1} (x) = 1 + 7 x

f_{2} (x) = - 1 + 7 x

Um die Schnittpunkte zu finden, löse

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

1 + 7 x = - 1 + 7 x : x = - \frac{1}{7}

1 + 7 x = - 1 + x : x = 9

- 1 + 7 x = - 1 + x : x = 0

= \int_{- \frac{1}{7}}^{0} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{0}^{9} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- \frac{1}{7}}^{0} 1 + 7 x - (- 1 + 7 x) d x + \int_{0}^{9} 1 + 7 x - (- 1 + x) d x

\int_{- \frac{1}{7}}^{0} 1 + 7 x - (- 1 + 7 x) d x = \frac{4}{21}

\int_{0}^{9} 1 + 7 x - (- 1 + x) d x = \frac{103}{6}

= \frac{4}{21} + \frac{103}{6}

Vereinfache

= \frac{243}{14}

Graph

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