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+6y,x=y

Solution

area

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

Solution

\frac{125}{6}

+1

Decimal Notation

20.83333 \dots

Solution steps

Isolate

y

for

x = y^{2} + 6 y : y = - 3 + x + 9, y = - x + 9 - 3

Isolate

y

for

x = y : y = x

f_{1} (x) = - 3 + x + 9

f_{2} (x) = - x + 9 - 3

To find the intersection points solve

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

- 3 + x + 9 = - x + 9 - 3 : x = - 9

- 3 + x + 9 = x : x = 0

- x + 9 - 3 = x : x = - 5

= \int_{- 9}^{- 5} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{- 5}^{0} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 9}^{- 5} - 3 + x + 9 - (- x + 9 - 3) d x + \int_{- 5}^{0} - 3 + x + 9 - x d x

\int_{- 9}^{- 5} - 3 + x + 9 - (- x + 9 - 3) d x = \frac{32}{3}

\int_{- 5}^{0} - 3 + x + 9 - x d x = \frac{61}{6}

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

Simplify

= \frac{125}{6}

Popular Examples

integral from 0 to x of 4tan(t)

\int_{0}^{x} 4 tan (t) d t

y^{''}+9y=e^{3x}

y^{^{''}} + 9 y = e^{3 x}

(\partial)/(\partial x)(sin^2(xy))

\frac{\partial}{\partial x} (sin^{2} (x y))

121y^{''}+44y^'+4y=0

121 y^{^{''}} + 44 y^{^{'}} + 4 y = 0

inverse oflaplace 1/(s(s^2+4))inverse laplace

\frac{1}{s ( s ^{2} + 4 )}

Frequently Asked Questions (FAQ)

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