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

\frac{2}{3}

+1

Decimal

0.66666 \dots

Solution steps

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

Expand

x (x - 1) : x^{2} - x

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

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

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

\int_{0}^{2} x d x = 2

= \frac{8}{3} - 2

Simplify

\frac{8}{3} - 2 : \frac{2}{3}

= \frac{2}{3}

Graph

Popular Examples

integral from 0 to pi/4 of sin^7(y)

\int_{0}^{\frac{π}{4}} sin^{7} (y) d y

integral from 0 to 1 of 17xe^x

\int_{0}^{1} 17 x e^{x} d x

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

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

integral from 0 to 2pi of (cos^2(θ))

\int_{0}^{2 π} (cos^{2} (θ)) d θ

integral from 0 to 7 of |x-4|

\int_{0}^{7} ∣ 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 2/3