en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

area (y^2)/2 =x,x=2y

Solution

area

\frac{y ^{2}}{2} = x, x = 2 y

Solution

\frac{16}{3}

+1

Decimal Notation

5.33333 \dots

Solution steps

Isolate

y

for

\frac{y ^{2}}{2} = x : y = 2 x, y = - 2 x

Isolate

y

for

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

f_{1} (x) = 2 x

f_{2} (x) = - 2 x

To find the intersection points solve

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

2 x = - 2 x : x = 0

2 x = \frac{x}{2} : x = 8, x = 0

- 2 x = \frac{x}{2} : x = 0

= \int_{0}^{8} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{0}^{8} 2 x - \frac{x}{2} d x

\int_{0}^{8} 2 x - \frac{x}{2} d x = \frac{16}{3}

= \frac{16}{3}

Popular Examples

integral of 5(9x-4)^4

\int 5 (9 x - 4)^{4} d x

integral of (10^x-1/(sqrt(x)))

\int (1 0^{x} - \frac{1}{x}) d x

derivative of x^2+6x+10

\frac{d}{d x} (x^{2} + 6 x + 10)

integral of 6x^4-6x^3+5x^2+C

\int 6 x^{4} - 6 x^{3} + 5 x^{2} + C d x

inverse oflaplace (50)/(1-3s^2)inverse laplace

\frac{50}{1 - 3 s ^{2}}

Frequently Asked Questions (FAQ)

What is area (y^2)/2 =x,x=2y ?
The answer to area (y^2)/2 =x,x=2y is 16/3