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Beliebt Rechnen >

fläche x=y^2-2y,x-y-4=0

Lösung

fläche

x = y^{2} - 2 y, x - y - 4 = 0

Lösung

\frac{125}{6}

+1

Dezimale

20.83333 \dots

Schritte zur Lösung

Stelle

y

nach

x = y^{2} - 2 y

um:

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

Stelle

y

nach

x - y - 4 = 0

um:

y = x - 4

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

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

Um die Schnittpunkte zu finden, löse

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

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

1 + x + 1 = x - 4 : x = 8

1 - x + 1 = x - 4 : x = 3

= \int_{- 1}^{3} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{3}^{8} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 1}^{3} 1 + x + 1 - (1 - x + 1) d x + \int_{3}^{8} 1 + x + 1 - (x - 4) d x

\int_{- 1}^{3} 1 + x + 1 - (1 - x + 1) d x = \frac{32}{3}

\int_{3}^{8} 1 + x + 1 - (x - 4) d x = \frac{61}{6}

= \frac{32}{3} + \frac{61}{6}

Vereinfache

= \frac{125}{6}

Graph

Beliebte Beispiele

derivative f(x)=(x^3-8)/(x^2-4)

d er i v a t i v e f (x) = \frac{x ^{3} - 8}{x ^{2} - 4}

derivative of x^{1/10}

\frac{d}{d x} (x^{\frac{1}{10}})

integral of u^2cos(u)

\int u^{2} cos (u) d u

integral of x^4ln(9x)

\int x^{4} ln (9 x) d x

y^{''}+4y^'-3y=x

y^{^{''}} + 4 y^{^{'}} - 3 y = x