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Beliebt Rechnen >

fläche x=y^2+1,x-y=1

Lösung

fläche

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

Lösung

\frac{1}{6}

+1

Dezimale

0.16666 \dots

Schritte zur Lösung

Stelle

y

nach

x = y^{2} + 1

um:

y = x - 1, y = - x - 1

Stelle

y

nach

x - y = 1

um:

y = - 1 + x

f_{1} (x) = x - 1

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

Um die Schnittpunkte zu finden, löse

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

x - 1 = - x - 1 : x = 1

x - 1 = - 1 + x : x = 2, x = 1

- x - 1 = - 1 + x : x = 1

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

= \int_{1}^{2} x - 1 - (- 1 + x) d x

\int_{1}^{2} x - 1 - (- 1 + x) d x = \frac{1}{6}

= \frac{1}{6}

Graph

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