What is area y=x-2,x=y^2 ?

The answer to area y=x-2,x=y^2 is 9/2

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

area

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

\frac{9}{2}

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 = 4

x - 2 = - x : x = 1

x = - x : x = 0

= \int_{0}^{1} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{1}^{4} ∣ f_{1} (x) - f_{2} (x) ∣ d x

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

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

\int_{1}^{4} x - 2 - x d x = \frac{19}{6}

= \frac{4}{3} + \frac{19}{6}

Simplify

= \frac{9}{2}

\int_{- 1}^{1} (1 - x^{2})^{\frac{3}{2}} d x

\frac{x}{6 x - 4}, at x = 9

\frac{\partial}{\partial x} (2 x^{4} y z^{3})

x \to 0 - lim (\frac{6}{5 x ^{\frac{1}{3}}})