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

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

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

area

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

\frac{9}{2}

Decimal Notation

4.5

Solution steps

Isolate

y

for

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

Isolate

y

for

x = - y : y = - x

f_{1} (x) = - x + 2

f_{2} (x) = - - x + 2

To find the intersection points solve

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

- x + 2 = - - x + 2 : x = 2

- x + 2 = - x : x = - 2

- - x + 2 = - x : x = 1

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

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

\int_{- 2}^{1} - x + 2 - (- x) d x = \frac{19}{6}

\int_{1}^{2} - - x + 2 - - x + 2 d x = \frac{4}{3}

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

Simplify

= \frac{9}{2}

\int_{0}^{\infty} \frac{8}{x ^{2} + 4} d x

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y = x x, (1, 1)

\frac{d}{d x} (\frac{x}{sin ( x )})

\frac{\partial}{\partial x} (x^{\frac{1}{4}})