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Popular Calculus >

area x+6y=8,x+8=y^2

Solution

area

x + 6 y = 8, x + 8 = y^{2}

Solution

\frac{500}{3}

+1

Decimal

166.66666 \dots

Solution steps

Isolate

y

for

x + 6 y = 8 : y = \frac{8 - x}{6}

Isolate

y

for

x + 8 = y^{2} : y = x + 8, y = - x + 8

f_{1} (x) = \frac{8 - x}{6}

f_{2} (x) = x + 8

To find the intersection points solve

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

\frac{8 - x}{6} = x + 8 : x = - 4

\frac{8 - x}{6} = - x + 8 : x = 56

x + 8 = - x + 8 : x = - 8

= \int_{- 8}^{- 4} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{- 4}^{56} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 8}^{- 4} x + 8 - (- x + 8) d x + \int_{- 4}^{56} \frac{8 - x}{6} - (- x + 8) d x

\int_{- 8}^{- 4} x + 8 - (- x + 8) d x = \frac{32}{3}

\int_{- 4}^{56} \frac{8 - x}{6} - (- x + 8) d x = 156

= \frac{32}{3} + 156

Simplify

= \frac{500}{3}

Graph

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Frequently Asked Questions (FAQ)

What is area x+6y=8,x+8=y^2 ?
The answer to area x+6y=8,x+8=y^2 is 500/3