What is area y^2=2x-2,y=x-5 ?

The answer to area y^2=2x-2,y=x-5 is 18

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area y^2=2x-2,y=x-5

area

y^{2} = 2 x - 2, y = x - 5

18

Solution steps

Isolate

y

for

y^{2} = 2 x - 2 : y = 2 x - 2, y = - 2 x - 2

f_{1} (x) = 2 x - 2

f_{2} (x) = - 2 x - 2

To find the intersection points solve

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

2 x - 2 = - 2 x - 2 : x = 1

2 x - 2 = x - 5 : x = 9

- 2 x - 2 = x - 5 : x = 3

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

= \int_{1}^{3} 2 x - 2 - (- 2 x - 2) d x + \int_{3}^{9} 2 x - 2 - (x - 5) d x

\int_{1}^{3} 2 x - 2 - (- 2 x - 2) d x = \frac{16}{3}

\int_{3}^{9} 2 x - 2 - (x - 5) d x = \frac{38}{3}

= \frac{16}{3} + \frac{38}{3}

Simplify

= 18

\frac{\partial}{\partial x} (cos (x^{2} y))

\int - 2 x + 18 x^{2} - 4 x^{3} + 18 d x

x \to 0 + lim (e^{- \frac{2}{x}})

\frac{\partial}{\partial x} (\frac{5 x}{y})

[x + (x + sin^{2} (x))^{7}]^{6}