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Popular Calculus >

area 4x+y^2=9,x=2y

Solution

area

4 x + y^{2} = 9, x = 2 y

Solution

\frac{125}{3}

+1

Decimal

41.66666 \dots

Solution steps

Isolate

y

for

4 x + y^{2} = 9 : y = 9 - 4 x, y = - 9 - 4 x

Isolate

y

for

x = 2 y : y = \frac{x}{2}

f_{1} (x) = 9 - 4 x

f_{2} (x) = - 9 - 4 x

To find the intersection points solve

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

9 - 4 x = - 9 - 4 x : x = \frac{9}{4}

9 - 4 x = \frac{x}{2} : x = 2

- 9 - 4 x = \frac{x}{2} : x = - 18

= \int_{- 18}^{2} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{2}^{\frac{9}{4}} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{- 18}^{2} - 9 - 4 x - \frac{x}{2} d x + \int_{2}^{\frac{9}{4}} 9 - 4 x - (- 9 - 4 x) d x

\int_{- 18}^{2} - 9 - 4 x - \frac{x}{2} d x = \frac{124}{3}

\int_{2}^{\frac{9}{4}} 9 - 4 x - (- 9 - 4 x) d x = \frac{1}{3}

= \frac{124}{3} + \frac{1}{3}

Simplify

= \frac{125}{3}

Graph

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Frequently Asked Questions (FAQ)

What is area 4x+y^2=9,x=2y ?
The answer to area 4x+y^2=9,x=2y is 125/3