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Popular >

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

Solution

area

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

Solution

\frac{1}{3}

+1

Decimal

0.33333 \dots

Solution steps

Isolate

y

for

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

f_{1} (x) = x^{2}

f_{2} (x) = x

To find the intersection points solve

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

x^{2} = x : x = 0, x = 1

x^{2} = - x : x = 0

x = - x : x = 0

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

= \int_{0}^{1} x^{2} - x d x

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

= \frac{1}{3}

Graph

Popular Examples

derivative of f(x)=5x-x^2 derivative of

f (x) = 5 x - x^{2}

y^{''}-10y+2y=0

y^{^{''}} - 10 y + 2 y = 0

x^{^{'}} + 3 x = 0

(\partial)/(\partial x)(x^6y-6x^2y^2)

\frac{\partial}{\partial x} (x^{6} y - 6 x^{2} y^{2})

integral from 1 to 0 of (4-5x^2)

\int_{1}^{0} (4 - 5 x^{2}) d x

Frequently Asked Questions (FAQ)

What is area y=x^2,y^2=x ?
The answer to area y=x^2,y^2=x is 1/3