What is area y=sqrt(x),y=x-2,y=0 ?

The answer to area y=sqrt(x),y=x-2,y=0 is 10/3

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area y=sqrt(x),y=x-2,y=0

area

y = x, y = x - 2, y = 0

\frac{10}{3}

Decimal

3.33333 \dots

Solution steps

To find the intersection points solve

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

x = x - 2 : x = 4

x = 0 : x = 0

x - 2 = 0 : x = 2

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

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

\int_{0}^{2} x - 0 d x = \frac{4 2}{3}

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

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

Simplify

= \frac{10}{3}

What is area y=sqrt(x),y=x-2,y=0 ?
The answer to area y=sqrt(x),y=x-2,y=0 is 10/3