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Popular >

area x+2y=9,x+6=y^2

Solution

area

x + 2 y = 9, x + 6 = y^{2}

Solution

\frac{256}{3}

+1

Decimal Notation

85.33333 \dots

Solution steps

Isolate

y

for

x + 2 y = 9 : y = \frac{9 - x}{2}

Isolate

y

for

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

f_{1} (x) = \frac{9 - x}{2}

f_{2} (x) = x + 6

To find the intersection points solve

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

\frac{9 - x}{2} = x + 6 : x = 3

\frac{9 - x}{2} = - x + 6 : x = 19

x + 6 = - x + 6 : x = - 6

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

= \int_{- 6}^{3} x + 6 - (- x + 6) d x + \int_{3}^{19} \frac{9 - x}{2} - (- x + 6) d x

\int_{- 6}^{3} x + 6 - (- x + 6) d x = 36

\int_{3}^{19} \frac{9 - x}{2} - (- x + 6) d x = \frac{148}{3}

= 36 + \frac{148}{3}

Simplify

= \frac{256}{3}

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Frequently Asked Questions (FAQ)

What is area x+2y=9,x+6=y^2 ?
The answer to area x+2y=9,x+6=y^2 is 256/3