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 2 of x|x-1|

Solution

\int_{0}^{2} x ∣ x - 1 ∣ d x

Solution

1

Solution steps

\int_{0}^{2} x ∣ x - 1 ∣ d x

Eliminate Absolutes

= \int_{0}^{1} x (- x + 1) d x + \int_{1}^{2} x (x - 1) d x

\int_{0}^{1} x (- x + 1) d x = \frac{1}{6}

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

= \frac{1}{6} + \frac{5}{6}

Simplify

\frac{1}{6} + \frac{5}{6} : 1

= 1

Graph

Popular Examples

integral from 0 to 1 of e^xsqrt(1-x)

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

integral from 0 to 2 of e^{x^2-x}

\int_{0}^{2} e^{x^{2} - x} d x

integral from-2 to 2 of x^2+3

\int_{- 2}^{2} x^{2} + 3 d x

integral from 0 to y of 1/y

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

integral from 0 to 3 of x^3sqrt(81-x^4)

\int_{0}^{3} x^{3} 81 - x^{4} d x

Frequently Asked Questions (FAQ)

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