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

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

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

area

\frac{10}{3}

Decimal

3.33333 \dots

Solution steps

To find the intersection points solve

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

- x = 2 - x : x = - 2

- x = 0 : x = 0

2 - x = 0 : x = 2

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

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

\int_{- 2}^{0} - x - 2 - x d x = - 2 + \frac{16 - 4 2}{3}

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

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

Simplify

= \frac{10}{3}

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