What is area x=y^2+4y-22,x=3y+8 ?

The answer to area x=y^2+4y-22,x=3y+8 is 1331/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

area x=y^2+4y-22,x=3y+8

area

x = y^{2} + 4 y - 22, x = 3 y + 8

\frac{1331}{6}

Decimal Notation

221.83333 \dots

Solution steps

Isolate

y

for

x = y^{2} + 4 y - 22 : y = - 2 + x + 26, y = - x + 26 - 2

Isolate

y

for

x = 3 y + 8 : y = \frac{x - 8}{3}

f_{1} (x) = - 2 + x + 26

f_{2} (x) = - x + 26 - 2

To find the intersection points solve

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

- 2 + x + 26 = - x + 26 - 2 : x = - 26

- 2 + x + 26 = \frac{x - 8}{3} : x = 23

- x + 26 - 2 = \frac{x - 8}{3} : x = - 10

= \int_{- 26}^{- 10} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{- 10}^{23} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 26}^{- 10} - 2 + x + 26 - (- x + 26 - 2) d x + \int_{- 10}^{23} - 2 + x + 26 - \frac{x - 8}{3} d x

\int_{- 26}^{- 10} - 2 + x + 26 - (- x + 26 - 2) d x = \frac{256}{3}

\int_{- 10}^{23} - 2 + x + 26 - \frac{x - 8}{3} d x = \frac{273}{2}

= \frac{256}{3} + \frac{273}{2}

Simplify

= \frac{1331}{6}

x - tan (x)

x (x + y) \frac{d y}{d x} = y (x - y)

4 x + 9

n = 1 \sum \infty 8 - 7 (0.8)^{n}

x \to 17 lim (3 x + 2)

What is area x=y^2+4y-22,x=3y+8 ?
The answer to area x=y^2+4y-22,x=3y+8 is 1331/6