fläche x=y^2,y=x-2

Lösung

fläche

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

\frac{9}{2}

Dezimale

4.5

Schritte zur Lösung

Stelle

y

nach

x = y^{2}

um:

y = x, y = - x

f_{1} (x) = x

f_{2} (x) = - x

Um die Schnittpunkte zu finden, löse

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

x = - x : x = 0

x = x - 2 : x = 4

- x = x - 2 : x = 1

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

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

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

\int_{1}^{4} x - (x - 2) d x = \frac{19}{6}

= \frac{4}{3} + \frac{19}{6}

Vereinfache

= \frac{9}{2}

x \to 0 lim (∣ x ∣ x)

\int x \cdot x - 1 d x

x \to 0 lim (s g (s, x) n (x))

\int sin (5 x) d (5 x) d x

ma c l a u r in 2 sin (x^{2})