de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

fläche 4x,4x+1, 3/(x-1)

Lösung

fläche

4 x, 4 x + 1, \frac{3}{x - 1}

Lösung

- \frac{24 ln ( \frac{73 - 5}{4} ) + 24 ln ( 2 ( \frac{3 + 73}{8} - 1 ) ) + 32 - 5 73}{8}

+1

Dezimale

2.06622 \dots

Schritte zur Lösung

Um die Schnittpunkte zu finden, löse

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

4 x = 4 x + 1 :

Keine Lösung

4 x = \frac{3}{x - 1} : x = \frac{3}{2}, x = - \frac{1}{2}

4 x + 1 = \frac{3}{x - 1} : x = \frac{3 + 73}{8}, x = \frac{3 - 73}{8}

= \int_{\frac{3 - 73}{8}}^{- \frac{1}{2}} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{- \frac{1}{2}}^{\frac{3 + 73}{8}} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{\frac{3 + 73}{8}}^{\frac{3}{2}} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{\frac{3 - 73}{8}}^{- \frac{1}{2}} 4 x + 1 - \frac{3}{x - 1} d x + \int_{- \frac{1}{2}}^{\frac{3 + 73}{8}} ∣ 4 x - (4 x + 1) ∣ d x + \int_{\frac{3 + 73}{8}}^{\frac{3}{2}} 4 x - \frac{3}{x - 1} d x

\int_{\frac{3 - 73}{8}}^{- \frac{1}{2}} 4 x + 1 - \frac{3}{x - 1} d x = - 3 ln (\frac{73 - 5}{4}) + \frac{5 73 - 47}{16}

\int_{- \frac{1}{2}}^{\frac{3 + 73}{8}} ∣ 4 x - (4 x + 1) ∣ d x = \frac{3 + 73}{8} + \frac{1}{2}

\int_{\frac{3 + 73}{8}}^{\frac{3}{2}} 4 x - \frac{3}{x - 1} d x = - 4 (\frac{9}{8} - \frac{41 + 3 73}{64}) - 3 ln (2 (\frac{3 + 73}{8} - 1))

= - 3 ln (\frac{73 - 5}{4}) + \frac{5 73 - 47}{16} + \frac{3 + 73}{8} + \frac{1}{2} - 4 (\frac{9}{8} - \frac{41 + 3 73}{64}) - 3 ln (2 (\frac{3 + 73}{8} - 1))

Vereinfache

= - \frac{24 ln ( \frac{73 - 5}{4} ) + 24 ln ( 2 ( \frac{3 + 73}{8} - 1 ) ) + 32 - 5 73}{8}

Graph

Beliebte Beispiele

limit as x approaches 2 of (x^3-6x^2+12x-8)/(x^4-4x^3+16x-16)

x \to 2 lim (\frac{x ^{3} - 6 x ^{2} + 12 x - 8}{x ^{4} - 4 x ^{3} + 16 x - 16})

derivative y=x^2+2x-6

d er i v a t i v e y = x^{2} + 2 x - 6

derivative of ae^x+be^{-9x}

\frac{d}{d x} (a e^{x} + b e^{- 9 x})

(\partial)/(\partial v)(u*cos(v))

\frac{\partial}{\partial v} (u \cdot cos (v))

integral of (x-2)^3

\int (x - 2)^{3} d x