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Popular >

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

Solution

area

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

Solution

\frac{9}{2}

+1

Decimal

4.5

Solution steps

Isolate

y

for

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

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

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

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

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

Simplify

= \frac{9}{2}

Graph

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Frequently Asked Questions (FAQ)

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