fläche y^2=x-2,y=x-4

Lösung

fläche

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

\frac{9}{2}

Dezimale

4.5

Schritte zur Lösung

Stelle

y

nach

y^{2} = x - 2

um:

y = x - 2, y = - x - 2

f_{1} (x) = x - 2

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

Um die Schnittpunkte zu finden, löse

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

x - 2 = - x - 2 : x = 2

x - 2 = x - 4 : x = 6

- x - 2 = x - 4 : x = 3

= \int_{2}^{3} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{3}^{6} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{2}^{3} x - 2 - (- x - 2) d x + \int_{3}^{6} x - 2 - (x - 4) d x

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

\int_{3}^{6} x - 2 - (x - 4) d x = \frac{19}{6}

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

Vereinfache

= \frac{9}{2}

\int (sec (2 x) + tan (2 x)) d x

d er i v a t i v e f (x) = \frac{2 t + 1}{t + 3}

a re a y = 2 x^{2} + 3, (0, 3)

\int \frac{x ^{2} + 1}{1 - x ^{2}} d x

x \to \frac{5 π}{6} lim (sin (x))