fläche x=((y-2)^2)/3 ,y=8-x

Lösung

fläche

x = \frac{( y - 2 ) ^{2}}{3}, y = 8 - x

\frac{81}{2}

Dezimale

40.5

Schritte zur Lösung

Stelle

y

nach

x = \frac{( y - 2 ) ^{2}}{3}

um:

y = 3 x + 2, y = - 3 x + 2

f_{1} (x) = 3 x + 2

f_{2} (x) = - 3 x + 2

Um die Schnittpunkte zu finden, löse

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

3 x + 2 = - 3 x + 2 : x = 0

3 x + 2 = 8 - x : x = 3

- 3 x + 2 = 8 - x : x = 12

= \int_{0}^{3} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{3}^{12} ∣ f_{2} (x) - f_{3} (x) ∣ d x

= \int_{0}^{3} 3 x + 2 - (- 3 x + 2) d x + \int_{3}^{12} - 3 x + 2 - (8 - x) d x

\int_{0}^{3} 3 x + 2 - (- 3 x + 2) d x = 12

\int_{3}^{12} - 3 x + 2 - (8 - x) d x = \frac{57}{2}

= 12 + \frac{57}{2}

Vereinfache

= \frac{81}{2}

\frac{d}{d x} ((x^{2} + 2)^{- 5} cos (x))

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

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

\int (2 x^{3} + 1)^{2} d x

\frac{d}{d x} (x + 1 + cos (x^{2}))