en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

area x=y(2-y),x=-y

Solution

area

x = y (2 - y), x = - y

Solution

\frac{9}{2}

+1

Decimal Notation

4.5

Solution steps

Isolate

y

for

x = y (2 - y) : y = 1 - - x + 1, y = - x + 1 + 1

Isolate

y

for

x = - y : y = - x

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

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

To find the intersection points solve

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

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

1 - - x + 1 = - x : x = 0

- x + 1 + 1 = - x : x = - 3

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

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

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

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

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

Simplify

= \frac{9}{2}

Popular Examples

limit as x approaches 343 of x^{2/3}

x \to 343 lim (x^{\frac{2}{3}})

integral from-2 to 3 of (41)/(x^4)

\int_{- 2}^{3} \frac{41}{x ^{4}} d x

derivative of f(x)=x^2arctan(x3^x)derivative of

f (x) = x^{2} arctan (x 3^{x})

integral from 0 to 1 of 2pix(4e^{-x^2})

\int_{0}^{1} 2 π x (4 e^{- x^{2}}) d x

y = ln (3^{3 x})

Frequently Asked Questions (FAQ)

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