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Popular >

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

Solution

area

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

Solution

\frac{1}{3}

+1

Decimal Notation

0.33333 \dots

Solution steps

Isolate

y

for

x = y^{2} : 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}

Popular Examples

3xy^'-15y=x^{-1}

3 x y^{^{'}} - 15 y = x^{- 1}

sum from n=9 to infinity of (1/7)^n

n = 9 \sum \infty (\frac{1}{7})^{n}

integral from-infinity to 0 of 0

\int_{- \infty}^{0} 0 d x

limit as x approaches 9 of 1/(sqrt(x)+3)

x \to 9 lim (\frac{1}{x + 3})

integral from 2 to 3 of tsqrt(t-2)

\int_{2}^{3} t t - 2 d t

Frequently Asked Questions (FAQ)

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