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Popular >

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

Solution

area

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

Solution

9

Solution steps

Isolate

y

for

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

f_{1} (x) = 2 x

f_{2} (x) = - 2 x

To find the intersection points solve

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

2 x = - 2 x : x = 0

2 x = 2 x - 4 : x = 4

- 2 x = 2 x - 4 : x = 1

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

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

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

\int_{1}^{4} 2 x - (2 x - 4) d x = \frac{19}{3}

= \frac{8}{3} + \frac{19}{3}

Simplify

= 9

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\int \frac{- 1}{y ^{2}} d y

Frequently Asked Questions (FAQ)

What is area y^2=4x,y=2x-4 ?
The answer to area y^2=4x,y=2x-4 is 9