What is area f(x)=sqrt(x),g(x)=2,h(x)=x ?

The answer to area f(x)=sqrt(x),g(x)=2,h(x)=x is 1

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area f(x)=sqrt(x),g(x)=2,h(x)=x

area

f (x) = x, g (x) = 2, h (x) = x

1

Solution steps

To find the intersection points solve

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

x = 2 : x = 4

x = x : x = 1, x = 0

2 = x : x = 2

= \int_{0}^{1} ∣ g (x) - f_{3} (x) ∣ d x + \int_{1}^{2} ∣ g (x) - f_{3} (x) ∣ d x + \int_{2}^{4} ∣ h (x) - g (x) ∣ d x

= \int_{0}^{1} x - x d x + \int_{1}^{2} x - x d x + \int_{2}^{4} 2 - x d x

\int_{0}^{1} x - x d x = \frac{1}{6}

\int_{1}^{2} x - x d x = - \frac{4 2 - 2}{3} + \frac{3}{2}

\int_{2}^{4} 2 - x d x = 4 - \frac{16 - 4 2}{3}

= \frac{1}{6} - \frac{4 2 - 2}{3} + \frac{3}{2} + 4 - \frac{16 - 4 2}{3}

Simplify

= 1

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What is area f(x)=sqrt(x),g(x)=2,h(x)=x ?
The answer to area f(x)=sqrt(x),g(x)=2,h(x)=x is 1