en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

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

\int_{0}^{1} - x^{2} + x 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-1 to 1 of x^2+x^4sin(x)

integral from 0 to infinity of kte^{-kt}

integral from-5 to 0 of-x^2-5x

integral from pi to 3pi of sin(θ)

integral from 0 to 1 of 4-4x^3

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