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Popular Calculus >

area y^2=x,x=2y

Solution

area

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

Solution

\frac{4}{3}

+1

Decimal

1.33333 \dots

Solution steps

Isolate

y

for

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

Isolate

y

for

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

f_{1} (x) = x

f_{2} (x) = - x

To find the intersection points solve

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

x = - x : x = 0

x = \frac{x}{2} : x = 4, x = 0

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

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

= \int_{0}^{4} x - \frac{x}{2} d x

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

= \frac{4}{3}

Graph

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Frequently Asked Questions (FAQ)

What is area y^2=x,x=2y ?
The answer to area y^2=x,x=2y is 4/3