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Popular >

area x=2y,x=y^2-8

Solution

area

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

Solution

36

Solution steps

Isolate

y

for

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

Isolate

y

for

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

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

f_{2} (x) = x + 8

To find the intersection points solve

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

\frac{x}{2} = x + 8 : x = 8

\frac{x}{2} = - x + 8 : x = - 4

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

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

= \int_{- 8}^{- 4} x + 8 - (- x + 8) d x + \int_{- 4}^{8} \frac{x}{2} - x + 8 d x

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

\int_{- 4}^{8} \frac{x}{2} - x + 8 d x = \frac{76}{3}

= \frac{32}{3} + \frac{76}{3}

Simplify

= 36

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Frequently Asked Questions (FAQ)

What is area x=2y,x=y^2-8 ?
The answer to area x=2y,x=y^2-8 is 36