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Popular Calculus >

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

Solution

area

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

Solution

\frac{343}{6}

+1

Decimal

57.16666 \dots

Solution steps

Isolate

y

for

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

Isolate

y

for

x = y : y = x

f_{1} (x) = x + 12

f_{2} (x) = - x + 12

To find the intersection points solve

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

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

x + 12 = x : x = 4

- x + 12 = x : x = - 3

= \int_{- 12}^{- 3} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{- 3}^{4} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 12}^{- 3} x + 12 - (- x + 12) d x + \int_{- 3}^{4} x + 12 - x d x

\int_{- 12}^{- 3} x + 12 - (- x + 12) d x = 36

\int_{- 3}^{4} x + 12 - x d x = \frac{127}{6}

= 36 + \frac{127}{6}

Simplify

= \frac{343}{6}

Graph

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Frequently Asked Questions (FAQ)

What is area x=y^2-12,x=y ?
The answer to area x=y^2-12,x=y is 343/6