fläche y= 3/x ,y=9x,y= 1/(9x)

Lösung

fläche

y = \frac{3}{x}, y = 9 x, y = \frac{1}{9 x}

- \frac{26}{9} + 9 ln (3) + divergiert

Schritte zur Lösung

Um die Schnittpunkte zu finden, löse

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

\frac{3}{x} = 9 x : x = \frac{1}{3}, x = - \frac{1}{3}

\frac{3}{x} = \frac{1}{9 x} :

Keine Lösung für

x \in R

9 x = \frac{1}{9 x} : x = \frac{1}{9}, x = - \frac{1}{9}

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

= \int_{- \frac{1}{3}}^{- \frac{1}{9}} \frac{3}{x} - 9 x d x + \int_{- \frac{1}{9}}^{\frac{1}{9}} \frac{3}{x} - \frac{1}{9 x} d x + \int_{\frac{1}{9}}^{\frac{1}{3}} 9 x - \frac{3}{x} d x

\int_{- \frac{1}{3}}^{- \frac{1}{9}} \frac{3}{x} - 9 x d x = \frac{9}{2} ln (3) - \frac{13}{9}

\int_{- \frac{1}{9}}^{\frac{1}{9}} \frac{3}{x} - \frac{1}{9 x} d x =

divergiert

\int_{\frac{1}{9}}^{\frac{1}{3}} 9 x - \frac{3}{x} d x = - \frac{13}{9} + \frac{9}{2} ln (3)

= \frac{9}{2} ln (3) - \frac{13}{9} + divergiert - \frac{13}{9} + \frac{9}{2} ln (3)

Vereinfache

= - \frac{26}{9} + 9 ln (3) + divergiert

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) d x

\int \frac{22}{22 + e ^{x}} d x

\int \frac{2 x + 1}{x ^{2} - 2 x + 5} d x

\int csc^{4} (θ) d θ

d er i v a t i v e 6 t e^{- t}