What is area y=20-x,y=sqrt(x),y=1 ?

The answer to area y=20-x,y=sqrt(x),y=1 is 63/2

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area y=20-x,y=sqrt(x),y=1

area

y = 20 - x, y = x, y = 1

\frac{63}{2}

Decimal

31.5

Solution steps

To find the intersection points solve

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

20 - x = x : x = 16

20 - x = 1 : x = 19

x = 1 : x = 1

= \int_{1}^{16} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{16}^{19} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{1}^{16} x - 1 d x + \int_{16}^{19} ∣ 20 - x - 1 ∣ d x

\int_{1}^{16} x - 1 d x = 27

\int_{16}^{19} ∣ 20 - x - 1 ∣ d x = \frac{9}{2}

= 27 + \frac{9}{2}

Simplify

= \frac{63}{2}

What is area y=20-x,y=sqrt(x),y=1 ?
The answer to area y=20-x,y=sqrt(x),y=1 is 63/2