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Popular >

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

Solution

area

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

Solution

\frac{9}{8}

+1

Decimal Notation

1.125

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 = 4 x - 2 : x = 1

- 2 x = 4 x - 2 : x = \frac{1}{4}

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

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

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

\int_{\frac{1}{4}}^{1} 2 x - (4 x - 2) d x = \frac{19}{24}

= \frac{1}{3} + \frac{19}{24}

Simplify

= \frac{9}{8}

Popular Examples

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y = \frac{1}{x}, x = a

derivative of a/(y^{10)}derivative of

\frac{a}{y ^{10}}

f (x) = 4 x^{\frac{1}{2}}

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\int_{0}^{12} x e^{- x} d x

derivative of y=e^{3x}cos(2x)derivative of

y = e^{3 x} cos (2 x)

Frequently Asked Questions (FAQ)

What is area y^2=4x,y=4x-2 ?
The answer to area y^2=4x,y=4x-2 is 9/8