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Popular >

area y^2=2x,x=2y

Solution

area

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

Solution

\frac{16}{3}

+1

Decimal Notation

5.33333 \dots

Solution steps

Isolate

y

for

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

Isolate

y

for

x = 2 y : y = \frac{x}{2}

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 = \frac{x}{2} : x = 8, x = 0

- 2 x = \frac{x}{2} : x = 0

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

= \int_{0}^{8} 2 x - \frac{x}{2} d x

\int_{0}^{8} 2 x - \frac{x}{2} d x = \frac{16}{3}

= \frac{16}{3}

Popular Examples

x^2y^{''}+xy^'-4y=0

x^{2} y^{^{''}} + x y^{^{'}} - 4 y = 0

derivative of cos(x+cot(x)+csc(x)+3e^x)

\frac{d}{d x} (cos (x) + cot (x) + csc (x) + 3 e^{x})

sum from n=0 to infinity of (2/3)^{-n}

n = 0 \sum \infty (\frac{2}{3})^{- n}

derivative of f(x)=(7^x)/(x^3)derivative of

f (x) = \frac{7 ^{x}}{x ^{3}}

(\partial)/(\partial y)(x^3y^3)

\frac{\partial}{\partial y} (x^{3} y^{3})

Frequently Asked Questions (FAQ)

What is area y^2=2x,x=2y ?
The answer to area y^2=2x,x=2y is 16/3