en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 2 of x(2-x)

Solution

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

Solution

\frac{2}{3}

+1

Decimal Notation

0.66666 \dots

Solution steps

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

Expand

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

= \int_{1}^{2} 2 x - x^{2} 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_{1}^{2} 2 x d x - \int_{1}^{2} x^{2} d x

\int_{1}^{2} 2 x d x = 3

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

= 3 - \frac{7}{3}

Simplify

3 - \frac{7}{3} : \frac{2}{3}

= \frac{2}{3}

Popular Examples

integral from 0 to 1 of (85)/(x^5)

\int_{0}^{1} \frac{85}{x ^{5}} d x

derivative of x/(9+x)

\frac{d}{d x} (\frac{x}{9 + x})

derivative of f(x)=sqrt(x^2+10)derivative of

f (x) = x^{2} + 10

integral of sin^2(x/4)

\int sin^{2} (\frac{x}{4}) d x

y^{^{'}} + x y = x y^{- 1}

Frequently Asked Questions (FAQ)

What is the integral from 1 to 2 of x(2-x) ?
The integral from 1 to 2 of x(2-x) is 2/3