What is area y=x-3,y=sqrt(2x+2),y=-sqrt(2x+2) ?

The answer to area y=x-3,y=sqrt(2x+2),y=-sqrt(2x+2) is 18

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area y=x-3,y=sqrt(2x+2),y=-sqrt(2x+2)

area

y = x - 3, y = 2 x + 2, y = - 2 x + 2

18

Solution steps

To find the intersection points solve

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

x - 3 = 2 x + 2 : x = 7

x - 3 = - 2 x + 2 : x = 1

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

= \int_{- 1}^{1} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{1}^{7} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{- 1}^{1} 2 x + 2 - (- 2 x + 2) d x + \int_{1}^{7} x - 3 - 2 x + 2 d x

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

\int_{1}^{7} x - 3 - 2 x + 2 d x = \frac{38}{3}

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

Simplify

= 18

\int (\frac{2}{x}) d x

\int_{1}^{\infty} \frac{7}{x ^{3}} d x

\frac{\partial}{\partial x} (\frac{1}{x - 2})

\int x^{3} x^{4} + 6 d x

n = 2 \sum \infty \frac{2}{n ^{2} - n}

What is area y=x-3,y=sqrt(2x+2),y=-sqrt(2x+2) ?
The answer to area y=x-3,y=sqrt(2x+2),y=-sqrt(2x+2) is 18