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Popular >

area x+y=0,x=y^2+3y

Solution

area

x + y = 0, x = y^{2} + 3 y

Solution

\frac{32}{3}

+1

Decimal Notation

10.66666 \dots

Solution steps

Isolate

y

for

x + y = 0 : y = - x

Isolate

y

for

x = y^{2} + 3 y : y = \frac{- 3 + 9 + 4 x}{2}, y = \frac{- 3 - 9 + 4 x}{2}

f_{1} (x) = - x

f_{2} (x) = \frac{- 3 + 9 + 4 x}{2}

To find the intersection points solve

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

- x = \frac{- 3 + 9 + 4 x}{2} : x = 0

- x = \frac{- 3 - 9 + 4 x}{2} : x = 4

\frac{- 3 + 9 + 4 x}{2} = \frac{- 3 - 9 + 4 x}{2} : x = - \frac{9}{4}

= \int_{- \frac{9}{4}}^{0} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{0}^{4} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- \frac{9}{4}}^{0} \frac{- 3 + 9 + 4 x}{2} - \frac{- 3 - 9 + 4 x}{2} d x + \int_{0}^{4} - x - \frac{- 3 - 9 + 4 x}{2} d x

\int_{- \frac{9}{4}}^{0} \frac{- 3 + 9 + 4 x}{2} - \frac{- 3 - 9 + 4 x}{2} d x = \frac{9}{2}

\int_{0}^{4} - x - \frac{- 3 - 9 + 4 x}{2} d x = \frac{37}{6}

= \frac{9}{2} + \frac{37}{6}

Simplify

= \frac{32}{3}

Popular Examples

integral of ke^{-kx}

\int k e^{- k x} d x

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ln (x^{100})

integral from-2 to 2 of x^2

\int_{- 2}^{2} x^{2} d x

derivative of b/((1-(y/x)))derivative of

\frac{b}{( 1 - ( \frac{y}{x} ) )}

derivative of x^{2/3}-x^{1/3}derivative of

x^{\frac{2}{3}} - x^{\frac{1}{3}}

Frequently Asked Questions (FAQ)

What is area x+y=0,x=y^2+3y ?
The answer to area x+y=0,x=y^2+3y is 32/3