What is area y=x-4,y^2=2x ?

The answer to area y=x-4,y^2=2x is 18

Popular >

area y=x-4,y^2=2x

area

y = x - 4, y^{2} = 2 x

18

Solution steps

Isolate

y

for

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

f_{1} (x) = x - 4

f_{2} (x) = 2 x

To find the intersection points solve

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

x - 4 = 2 x : x = 8

x - 4 = - 2 x : x = 2

2 x = - 2 x : x = 0

= \int_{0}^{2} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{2}^{8} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{0}^{2} 2 x - (- 2 x) d x + \int_{2}^{8} x - 4 - 2 x d x

\int_{0}^{2} 2 x - (- 2 x) d x = \frac{16}{3}

\int_{2}^{8} x - 4 - 2 x d x = \frac{38}{3}

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

Simplify

= 18

x \to + 0 lim (x ln (\frac{1}{x}))

(sin (x)) (sec (x))

\int_{- 1}^{1} \frac{1}{2} (1 - x^{4}) d x

\int \frac{x ^{3} + 5 x + 1}{x ^{2} + 5} d x

\frac{\partial}{\partial x} (x e^{\frac{y}{x}})