en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

area x=2y,x=y^2-15

Solution

area

x = 2 y, x = y^{2} - 15

Solution

\frac{256}{3}

+1

Decimal

85.33333 \dots

Solution steps

Isolate

y

for

x = 2 y : y = \frac{x}{2}

Isolate

y

for

x = y^{2} - 15 : y = x + 15, y = - x + 15

f_{1} (x) = \frac{x}{2}

f_{2} (x) = x + 15

To find the intersection points solve

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

\frac{x}{2} = x + 15 : x = 10

\frac{x}{2} = - x + 15 : x = - 6

x + 15 = - x + 15 : x = - 15

= \int_{- 15}^{- 6} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{- 6}^{10} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{- 15}^{- 6} x + 15 - (- x + 15) d x + \int_{- 6}^{10} \frac{x}{2} - x + 15 d x

\int_{- 15}^{- 6} x + 15 - (- x + 15) d x = 36

\int_{- 6}^{10} \frac{x}{2} - x + 15 d x = \frac{148}{3}

= 36 + \frac{148}{3}

Simplify

= \frac{256}{3}

Graph

Popular Examples

limit as x approaches 0 of ((3+x)^3-9)/x

(\partial)/(\partial x)(zln(x))

integral of x^2e^{x/6}

(\partial)/(\partial x)(-xyz+54)

derivative of 3e^{x^2}

Frequently Asked Questions (FAQ)

What is area x=2y,x=y^2-15 ?
The answer to area x=2y,x=y^2-15 is 256/3