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

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

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

area

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

\frac{10}{3}

Decimal

3.33333 \dots

Solution steps

To find the intersection points solve

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

x = 0 : x = 0

x = x - 2 : x = 4

0 = x - 2 : x = 2

= \int_{0}^{2} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{2}^{4} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{0}^{2} x - 0 d x + \int_{2}^{4} x - (x - 2) d x

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

\int_{2}^{4} x - (x - 2) d x = \frac{16 - 4 2}{3} - 2

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

Simplify

= \frac{10}{3}

x \to 3 + lim (\frac{2}{x - 3})

y^{^{'}} = y - 4 y^{2}

y^{^{'}} = \frac{x ^{2}}{y ( 1 + x ^{3} )}

\frac{d}{d x} (\frac{1}{x ( ln ( x ) ) ^{2}})

\int \frac{( x - 2 ) 1 - x ^{2} + x}{1 - x ^{2}} d x

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