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Popular >

area x+y^2=4,x+y=2

Solution

area

x + y^{2} = 4, x + y = 2

Solution

\frac{9}{2}

+1

Decimal

4.5

Solution steps

Isolate

y

for

x + y^{2} = 4 : y = 4 - x, y = - 4 - x

Isolate

y

for

x + y = 2 : y = 2 - x

f_{1} (x) = 4 - x

f_{2} (x) = - 4 - x

To find the intersection points solve

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

4 - x = - 4 - x : x = 4

4 - x = 2 - x : x = 0

- 4 - x = 2 - x : x = 3

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

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

\int_{0}^{3} 4 - x - (2 - x) d x = \frac{19}{6}

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

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

Simplify

= \frac{9}{2}

Graph

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Frequently Asked Questions (FAQ)

What is area x+y^2=4,x+y=2 ?
The answer to area x+y^2=4,x+y=2 is 9/2