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Popular Calculus >

area 7x, 1/x ,x

Solution

area

7 x, \frac{1}{x}, x

Solution

ln (7)

+1

Decimal

1.94591 \dots

Solution steps

To find the intersection points solve

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

7 x = \frac{1}{x} : x = \frac{1}{7}, x = - \frac{1}{7}

7 x = x : x = 0

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

= \int_{- 1}^{- \frac{1}{7}} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{- \frac{1}{7}}^{0} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{0}^{\frac{1}{7}} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{\frac{1}{7}}^{1} ∣ f_{3} (x) - f_{2} (x) ∣ d x

= \int_{- 1}^{- \frac{1}{7}} \frac{1}{x} - x d x + \int_{- \frac{1}{7}}^{0} ∣ 7 x - x ∣ d x + \int_{0}^{\frac{1}{7}} ∣ 7 x - x ∣ d x + \int_{\frac{1}{7}}^{1} x - \frac{1}{x} d x

\int_{- 1}^{- \frac{1}{7}} \frac{1}{x} - x d x = \frac{1}{2} ln (7) - \frac{3}{7}

\int_{- \frac{1}{7}}^{0} ∣ 7 x - x ∣ d x = \frac{3}{7}

\int_{0}^{\frac{1}{7}} ∣ 7 x - x ∣ d x = \frac{3}{7}

\int_{\frac{1}{7}}^{1} x - \frac{1}{x} d x = - \frac{3}{7} + \frac{1}{2} ln (7)

= \frac{1}{2} ln (7) - \frac{3}{7} + \frac{3}{7} + \frac{3}{7} - \frac{3}{7} + \frac{1}{2} ln (7)

Simplify

= ln (7)

Graph

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Frequently Asked Questions (FAQ)

What is area 7x, 1/x ,x ?
The answer to area 7x, 1/x ,x is ln(7)