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Beliebt Rechnen >

fläche x+y=13,x+7=y^2

Lösung

fläche

x + y = 13, x + 7 = y^{2}

Lösung

\frac{243}{2}

+1

Dezimale

121.5

Schritte zur Lösung

Stelle

y

nach

x + y = 13

um:

y = 13 - x

Stelle

y

nach

x + 7 = y^{2}

um:

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

f_{1} (x) = 13 - x

f_{2} (x) = x + 7

Um die Schnittpunkte zu finden, löse

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

13 - x = x + 7 : x = 9

13 - x = - x + 7 : x = 18

x + 7 = - x + 7 : x = - 7

= \int_{- 7}^{9} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{9}^{18} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 7}^{9} x + 7 - (- x + 7) d x + \int_{9}^{18} 13 - x - (- x + 7) d x

\int_{- 7}^{9} x + 7 - (- x + 7) d x = \frac{256}{3}

\int_{9}^{18} 13 - x - (- x + 7) d x = \frac{217}{6}

= \frac{256}{3} + \frac{217}{6}

Vereinfache

= \frac{243}{2}

Graph

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