What is area y= 1/(sqrt(x)),y=x,y=2 ?

The answer to area y= 1/(sqrt(x)),y=x,y=2 is 1

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area y= 1/(sqrt(x)),y=x,y=2

area

y = \frac{1}{x}, y = x, y = 2

1

Solution steps

To find the intersection points solve

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

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

\frac{1}{x} = 2 : x = \frac{1}{4}

x = 2 : x = 2

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

= \int_{\frac{1}{4}}^{1} \frac{1}{x} - 2 d x + \int_{1}^{2} ∣ 2 - x ∣ d x

\int_{\frac{1}{4}}^{1} \frac{1}{x} - 2 d x = \frac{1}{2}

\int_{1}^{2} ∣ 2 - x ∣ d x = \frac{1}{2}

= \frac{1}{2} + \frac{1}{2}

Simplify

= 1

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What is area y= 1/(sqrt(x)),y=x,y=2 ?
The answer to area y= 1/(sqrt(x)),y=x,y=2 is 1