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Popular >

area 2/x ,8x, x/2

Solution

area

\frac{2}{x}, 8 x, \frac{x}{2}

Solution

8 ln (2)

+1

Solution steps

To find the intersection points solve

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

\frac{2}{x} = 8 x : x = \frac{1}{2}, x = - \frac{1}{2}

\frac{2}{x} = \frac{x}{2} : x = 2, x = - 2

8 x = \frac{x}{2} : x = 0

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

= \int_{- 2}^{- \frac{1}{2}} \frac{2}{x} - \frac{x}{2} d x + \int_{- \frac{1}{2}}^{0} \frac{x}{2} - 8 x d x + \int_{0}^{\frac{1}{2}} 8 x - \frac{x}{2} d x + \int_{\frac{1}{2}}^{2} \frac{2}{x} - \frac{x}{2} d x

\int_{- 2}^{- \frac{1}{2}} \frac{2}{x} - \frac{x}{2} d x = 4 ln (2) - \frac{15}{16}

\int_{- \frac{1}{2}}^{0} \frac{x}{2} - 8 x d x = \frac{15}{16}

\int_{0}^{\frac{1}{2}} 8 x - \frac{x}{2} d x = \frac{15}{16}

\int_{\frac{1}{2}}^{2} \frac{2}{x} - \frac{x}{2} d x = 4 ln (2) - \frac{15}{16}

= 4 ln (2) - \frac{15}{16} + \frac{15}{16} + \frac{15}{16} + 4 ln (2) - \frac{15}{16}

Simplify

= 8 ln (2)

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Frequently Asked Questions (FAQ)

What is area 2/x ,8x, x/2 ?
The answer to area 2/x ,8x, x/2 is 8ln(2)