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Popular >

area x=y,x=y^2

Solution

area

x = y, x = y^{2}

Solution

\frac{1}{6}

+1

Decimal

0.16666 \dots

Solution steps

Isolate

y

for

x = y : y = x

Isolate

y

for

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

f_{1} (x) = x

f_{2} (x) = x

To find the intersection points solve

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

x = x : x = 1, x = 0

x = - x : x = 0

x = - x : x = 0

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

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

\int_{0}^{1} x - x d x = \frac{1}{6}

= \frac{1}{6}

Graph

Popular Examples

integral of (19-19x)/(1-sqrt(x))

\int \frac{19 - 19 x}{1 - x} d x

integral of 3/(x^2sqrt(x^2+16))

\int \frac{3}{x ^{2} x ^{2} + 16} d x

sum from n=1 to infinity of 1/(n+1000)

n = 1 \sum \infty \frac{1}{n + 1000}

d/(dt)((3t^2)/(1+t^3))

\frac{d}{d t} (\frac{3 t ^{2}}{1 + t ^{3}})

derivative of x^3+6x^2+8x-96

\frac{d}{d x} (x^{3} + 6 x^{2} + 8 x - 96)

Frequently Asked Questions (FAQ)

What is area x=y,x=y^2 ?
The answer to area x=y,x=y^2 is 1/6