fläche x=y^2+6y,y=x

Lösung

fläche

x = y^{2} + 6 y, y = x

\frac{125}{6}

Dezimale

20.83333 \dots

Schritte zur Lösung

Stelle

y

nach

x = y^{2} + 6 y

um:

y = - 3 + x + 9, y = - x + 9 - 3

f_{1} (x) = - 3 + x + 9

f_{2} (x) = - x + 9 - 3

Um die Schnittpunkte zu finden, löse

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

- 3 + x + 9 = - x + 9 - 3 : x = - 9

- 3 + x + 9 = x : x = 0

- x + 9 - 3 = x : x = - 5

= \int_{- 9}^{- 5} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{- 5}^{0} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 9}^{- 5} - 3 + x + 9 - (- x + 9 - 3) d x + \int_{- 5}^{0} - 3 + x + 9 - x d x

\int_{- 9}^{- 5} - 3 + x + 9 - (- x + 9 - 3) d x = \frac{32}{3}

\int_{- 5}^{0} - 3 + x + 9 - x d x = \frac{61}{6}

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

Vereinfache

= \frac{125}{6}

n = 0 \sum \infty x^{n + 5}

x \to 4 + lim (\frac{7}{x - 4})

d er i v a t i v e f (x) = 1 + x

a re a \frac{1}{x}, \frac{1}{x ^{2}}, 2

\int \frac{sin ( t )}{t ^{2}} d t