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Popular >

area x=4y,x=y^2-12

Solution

area

x = 4 y, x = y^{2} - 12

Solution

\frac{256}{3}

+1

Decimal Notation

85.33333 \dots

Solution steps

Isolate

y

for

x = 4 y : y = \frac{x}{4}

Isolate

y

for

x = y^{2} - 12 : y = x + 12, y = - x + 12

f_{1} (x) = \frac{x}{4}

f_{2} (x) = x + 12

To find the intersection points solve

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

\frac{x}{4} = x + 12 : x = 24

\frac{x}{4} = - x + 12 : x = - 8

x + 12 = - x + 12 : x = - 12

= \int_{- 12}^{- 8} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{- 8}^{24} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{- 12}^{- 8} x + 12 - (- x + 12) d x + \int_{- 8}^{24} \frac{x}{4} - x + 12 d x

\int_{- 12}^{- 8} x + 12 - (- x + 12) d x = \frac{32}{3}

\int_{- 8}^{24} \frac{x}{4} - x + 12 d x = \frac{224}{3}

= \frac{32}{3} + \frac{224}{3}

Simplify

= \frac{256}{3}

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Frequently Asked Questions (FAQ)

What is area x=4y,x=y^2-12 ?
The answer to area x=4y,x=y^2-12 is 256/3