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Popular >

area x=y^2+6y,y=x

Solution

area

x = y^{2} + 6 y, y = x

Solution

\frac{125}{6}

+1

Decimal Notation

20.83333 \dots

Solution steps

Isolate

y

for

x = y^{2} + 6 y : y = - 3 + x + 9, y = - x + 9 - 3

f_{1} (x) = - 3 + x + 9

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

To find the intersection points solve

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

- 3 + x + 9 = - x + 9 - 3 : x = - 9

- 3 + x + 9 = x : x = 0

- x + 9 - 3 = x : x = - 5

= \int_{- 9}^{- 5} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{- 5}^{0} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 9}^{- 5} - 3 + x + 9 - (- x + 9 - 3) d x + \int_{- 5}^{0} - 3 + x + 9 - x d x

\int_{- 9}^{- 5} - 3 + x + 9 - (- x + 9 - 3) d x = \frac{32}{3}

\int_{- 5}^{0} - 3 + x + 9 - x d x = \frac{61}{6}

= \frac{32}{3} + \frac{61}{6}

Simplify

= \frac{125}{6}

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Frequently Asked Questions (FAQ)

What is area x=y^2+6y,y=x ?
The answer to area x=y^2+6y,y=x is 125/6