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Popular Calculus >

area x=6-y^2,x=y

Solution

area

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

Solution

\frac{125}{6}

+1

Decimal

20.83333 \dots

Solution steps

Isolate

y

for

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

Isolate

y

for

x = y : y = x

f_{1} (x) = - x + 6

f_{2} (x) = - - x + 6

To find the intersection points solve

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

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

- x + 6 = x : x = 2

- - x + 6 = x : x = - 3

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

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

\int_{- 3}^{2} - - x + 6 - x d x = \frac{61}{6}

\int_{2}^{6} - x + 6 - (- - x + 6) d x = \frac{32}{3}

= \frac{61}{6} + \frac{32}{3}

Simplify

= \frac{125}{6}

Graph

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Frequently Asked Questions (FAQ)

What is area x=6-y^2,x=y ?
The answer to area x=6-y^2,x=y is 125/6