en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

area y=x-1,y^2=2x+6

Solution

area

y = x - 1, y^{2} = 2 x + 6

Solution

18

Solution steps

Isolate

y

for

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

f_{1} (x) = x - 1

f_{2} (x) = 2 x + 6

To find the intersection points solve

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

x - 1 = 2 x + 6 : x = 5

x - 1 = - 2 x + 6 : x = - 1

2 x + 6 = - 2 x + 6 : x = - 3

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

= \int_{- 3}^{- 1} 2 x + 6 - (- 2 x + 6) d x + \int_{- 1}^{5} x - 1 - 2 x + 6 d x

\int_{- 3}^{- 1} 2 x + 6 - (- 2 x + 6) d x = \frac{16}{3}

\int_{- 1}^{5} x - 1 - 2 x + 6 d x = \frac{38}{3}

= \frac{16}{3} + \frac{38}{3}

Simplify

= 18

Graph

Popular Examples

t*(dy)/(dt)=t^3+11t^3y

derivative of 1/(x^3-4x)

integral of (27)/(27+e^x)

derivative of ((2+5z)/(5z))(15-2z)

Frequently Asked Questions (FAQ)

What is area y=x-1,y^2=2x+6 ?
The answer to area y=x-1,y^2=2x+6 is 18