What is area y=0,y=-x+5,y=sqrt(x+1) ?

The answer to area y=0,y=-x+5,y=sqrt(x+1) is 22/3

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area y=0,y=-x+5,y=sqrt(x+1)

area

y = 0, y = - x + 5, y = x + 1

\frac{22}{3}

Decimal Notation

7.33333 \dots

Solution steps

To find the intersection points solve

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

0 = - x + 5 : x = 5

0 = x + 1 : x = - 1

- x + 5 = x + 1 : x = 3

= \int_{- 1}^{3} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{3}^{5} ∣ f_{2} (x) - f_{1} (x) ∣ d x

= \int_{- 1}^{3} 0 - x + 1 d x + \int_{3}^{5} ∣ - x + 5 - 0 ∣ d x

\int_{- 1}^{3} 0 - x + 1 d x = \frac{16}{3}

\int_{3}^{5} ∣ - x + 5 - 0 ∣ d x = 2

= \frac{16}{3} + 2

Simplify

= \frac{22}{3}

- \frac{s - 2}{2 ( s ^{2} - 2 s + 2 )}

\int \frac{2 x}{x ^{2} + 1} d x

(12 - x) y^{2} = x^{3}, (6, 6)

\int (4 x^{3} + 2 x y^{2}) d x

x^{2} y^{^{'}} + 2 x y = ln (x)

What is area y=0,y=-x+5,y=sqrt(x+1) ?
The answer to area y=0,y=-x+5,y=sqrt(x+1) is 22/3