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Popular >

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

Solution

area

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

Solution

\frac{9}{2}

+1

Decimal

4.5

Solution steps

Isolate

y

for

x = y : y = x

Isolate

y

for

y^{2} - 2 y = x : y = 1 + x + 1, y = 1 - x + 1

f_{1} (x) = x

f_{2} (x) = 1 + x + 1

To find the intersection points solve

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

x = 1 + x + 1 : x = 3

x = 1 - x + 1 : x = 0

1 + x + 1 = 1 - x + 1 : x = - 1

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

= \int_{- 1}^{0} 1 + x + 1 - (1 - x + 1) d x + \int_{0}^{3} x - (1 + x + 1) d x

\int_{- 1}^{0} 1 + x + 1 - (1 - x + 1) d x = \frac{4}{3}

\int_{0}^{3} x - (1 + x + 1) d x = \frac{19}{6}

= \frac{4}{3} + \frac{19}{6}

Simplify

= \frac{9}{2}

Graph

Popular Examples

derivative of y=3x^2+2 derivative of

y = 3 x^{2} + 2

integral of (1/2-1/2 cos(2θ-pi/4))

\int (\frac{1}{2} - \frac{1}{2} cos (2 θ - \frac{π}{4})) d θ

laplacetransform 1+0.2t laplace transform

1 + 0.2 t

(d^4)/(dx^4)(8e^{-4x})

\frac{d ^{4}}{d x ^{4}} (8 e^{- 4 x})

(dy)/(dx)=y(3-y),y(0.2)=8

\frac{d y}{d x} = y (3 - y), y (0.2) = 8

Frequently Asked Questions (FAQ)

What is area x=y,y^2-2y=x ?
The answer to area x=y,y^2-2y=x is 9/2