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Popular >

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

Solution

area

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

Solution

\frac{125}{6}

+1

Decimal Notation

20.83333 \dots

Solution steps

Isolate

y

for

x = 4 - y^{2} : y = - x + 4, y = - - x + 4

Isolate

y

for

x = y - 2 : y = x + 2

f_{1} (x) = - x + 4

f_{2} (x) = - - x + 4

To find the intersection points solve

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

- x + 4 = - - x + 4 : x = 4

- x + 4 = x + 2 : x = 0

- - x + 4 = x + 2 : x = - 5

= \int_{- 5}^{0} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{0}^{4} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{- 5}^{0} - - x + 4 - (x + 2) d x + \int_{0}^{4} - x + 4 - (- - x + 4) d x

\int_{- 5}^{0} - - x + 4 - (x + 2) d x = \frac{61}{6}

\int_{0}^{4} - x + 4 - (- - x + 4) d x = \frac{32}{3}

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

Simplify

= \frac{125}{6}

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y^{^{'}} (x^{2} + 1) + 9 x (y - 1) = 0

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x \to 0 + lim (a x^{x} + 1)

\frac{d y}{d x} + 4 y = 3

Frequently Asked Questions (FAQ)

What is area x=4-y^2,x=y-2 ?
The answer to area x=4-y^2,x=y-2 is 125/6