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Popular >

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

Solution

area

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

Solution

\frac{9}{2}

+1

Decimal Notation

4.5

Solution steps

Isolate

y

for

x + y = 2 : y = 2 - x

Isolate

y

for

x = y^{2} - 2 y : y = 1 + x + 1, y = 1 - x + 1

f_{1} (x) = 2 - x

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

To find the intersection points solve

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

2 - x = 1 + x + 1 : x = 0

2 - x = 1 - x + 1 : x = 3

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

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

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

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

\int_{0}^{3} 2 - x - (1 - x + 1) d x = \frac{19}{6}

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

Simplify

= \frac{9}{2}

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y^{^{''}} + y = csc^{2} (x)

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\int x (x^{2} + 1)^{4} d x

Frequently Asked Questions (FAQ)

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