What is area y=12-x,y=sqrt(x),y=1 ?

The answer to area y=12-x,y=sqrt(x),y=1 is 34/3

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area y=12-x,y=sqrt(x),y=1

area

y = 12 - x, y = x, y = 1

\frac{34}{3}

Decimal Notation

11.33333 \dots

Solution steps

To find the intersection points solve

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

12 - x = x : x = 9

12 - x = 1 : x = 11

x = 1 : x = 1

= \int_{1}^{9} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{9}^{11} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{1}^{9} x - 1 d x + \int_{9}^{11} ∣ 12 - x - 1 ∣ d x

\int_{1}^{9} x - 1 d x = \frac{28}{3}

\int_{9}^{11} ∣ 12 - x - 1 ∣ d x = 2

= \frac{28}{3} + 2

Simplify

= \frac{34}{3}

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What is area y=12-x,y=sqrt(x),y=1 ?
The answer to area y=12-x,y=sqrt(x),y=1 is 34/3