What is area x-1,y^2=2x+6 ?

The answer to area x-1,y^2=2x+6 is 18

Popular >

area x-1,y^2=2x+6

area

x - 1, y^{2} = 2 x + 6

18

Solution steps

Isolate

y

for

y^{2} = 2 x + 6 : y = 2 x + 6, y = - 2 x + 6

f_{1} (x) = 2 x + 6

f_{2} (x) = - 2 x + 6

To find the intersection points solve

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

2 x + 6 = - 2 x + 6 : x = - 3

2 x + 6 = x - 1 : x = 5

- 2 x + 6 = x - 1 : x = - 1

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

= \int_{- 3}^{- 1} 2 x + 6 - (- 2 x + 6) d x + \int_{- 1}^{5} 2 x + 6 - (x - 1) d x

\int_{- 3}^{- 1} 2 x + 6 - (- 2 x + 6) d x = \frac{16}{3}

\int_{- 1}^{5} 2 x + 6 - (x - 1) d x = \frac{38}{3}

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

Simplify

= 18

\frac{d}{d x} (y - x - 2)

\frac{\partial}{\partial x} (x^{2} (1 + sin (\frac{1}{x})))

x \to 2.5 lim (g (x))

\int \frac{1}{t ^{2} + 6 t + 25} d t

(3, 2), (7, - 4)