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Popular >

area y=x^3,x=y^2

Solution

area

y = x^{3}, x = y^{2}

Solution

\frac{5}{12}

+1

Decimal Notation

0.41666 \dots

Solution steps

Isolate

y

for

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

f_{1} (x) = x^{3}

f_{2} (x) = x

To find the intersection points solve

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

x^{3} = x : x = 0, x = 1

x^{3} = - x : x = 0

x = - x : x = 0

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

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

\int_{0}^{1} x^{3} - x d x = \frac{5}{12}

= \frac{5}{12}

Popular Examples

integral of ln(x/(x^2))

\int ln (\frac{x}{x ^{2}}) d x

f(x)=(cos(x))/x

f (x) = \frac{cos ( x )}{x}

derivative of-cos(3x)*3 derivative of

- cos (3 x) \cdot 3

integral of 1/(ax^2+bx)

\int \frac{1}{a x ^{2} + b x} d x

limit as x approaches 5 of 8x+|x-5|

x \to 5 lim (8 x + ∣ x - 5 ∣)

Frequently Asked Questions (FAQ)

What is area y=x^3,x=y^2 ?
The answer to area y=x^3,x=y^2 is 5/12