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Beliebt Rechnen >

fläche y^2=4x,4x-3y=4

Lösung

fläche

y^{2} = 4 x, 4 x - 3 y = 4

Lösung

\frac{125}{24}

+1

Dezimale

5.20833 \dots

Schritte zur Lösung

Stelle

y

nach

y^{2} = 4 x

um:

y = 2 x, y = - 2 x

Stelle

y

nach

4 x - 3 y = 4

um:

y = - \frac{4 - 4 x}{3}

f_{1} (x) = 2 x

f_{2} (x) = - 2 x

Um die Schnittpunkte zu finden, löse

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

2 x = - 2 x : x = 0

2 x = - \frac{4 - 4 x}{3} : x = 4

- 2 x = - \frac{4 - 4 x}{3} : x = \frac{1}{4}

= \int_{0}^{\frac{1}{4}} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{\frac{1}{4}}^{4} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{0}^{\frac{1}{4}} 2 x - (- 2 x) d x + \int_{\frac{1}{4}}^{4} 2 x - (- \frac{4 - 4 x}{3}) d x

\int_{0}^{\frac{1}{4}} 2 x - (- 2 x) d x = \frac{1}{3}

\int_{\frac{1}{4}}^{4} 2 x - (- \frac{4 - 4 x}{3}) d x = \frac{39}{8}

= \frac{1}{3} + \frac{39}{8}

Vereinfache

= \frac{125}{24}

Graph

Beliebte Beispiele

integral from 1 to 5 of x/(sqrt(2x-1))

\int_{1}^{5} \frac{x}{2 x - 1} d x

limit as x approaches 0 of cos(x)+sin(x)

x \to 0 lim (cos (x) + sin (x))

(dy)/(dx)=((y^2-1))/(x^2-1),y(7)=7

\frac{d y}{d x} = \frac{( y ^{2} - 1 )}{x ^{2} - 1}, y (7) = 7

y^{^{'}} = 8 x^{3} + 2 \frac{y}{x}

(dy)/(dt)=-2y,y(0)=2

\frac{d y}{d t} = - 2 y, y (0) = 2