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

The answer to area y=sqrt(x),y=2-x,y=0 is 7/6

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

area

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

\frac{7}{6}

Decimal

1.16666 \dots

Solution steps

To find the intersection points solve

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

x = 2 - x : x = 1

x = 0 : x = 0

2 - x = 0 : x = 2

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

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

\int_{0}^{1} x - 0 d x = \frac{2}{3}

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

= \frac{2}{3} + \frac{1}{2}

Simplify

= \frac{7}{6}

What is area y=sqrt(x),y=2-x,y=0 ?
The answer to area y=sqrt(x),y=2-x,y=0 is 7/6