en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of |x-y|

Solution

\int_{0}^{1} ∣ x - y ∣ d y

Solution

- x + \frac{1}{2}

Solution steps

\int_{0}^{1} ∣ x - y ∣ d y

Eliminate Absolutes

= \int_{0}^{1} - x + y d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{0}^{1} x d y + \int_{0}^{1} y d y

\int_{0}^{1} x d y = x

\int_{0}^{1} y d y = \frac{1}{2}

= - x + \frac{1}{2}

Popular Examples

integral from 1 to 3 of ((x^2+2)/x)

\int_{1}^{3} (\frac{x ^{2} + 2}{x}) d x

integral from 3 to 7 of 1/(sqrt(x^2-4))

\int_{3}^{7} \frac{1}{x ^{2} - 4} d x

integral from 0 to 1 of (e^{-x})/(x+1)

\int_{0}^{1} \frac{e ^{- x}}{x + 1} d x

integral from 0 to 2 of 5t

\int_{0}^{2} 5 t d t

integral from 0 to 3 of x/(1+4x^2)

\int_{0}^{3} \frac{x}{1 + 4 x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of |x-y| ?
The integral from 0 to 1 of |x-y| is -x+1/2