What is the integral from 2 to 4 of x((2x-3))/6 ?

The integral from 2 to 4 of x((2x-3))/6 is 29/9

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 4 of x((2x-3))/6

\int_{2}^{4} x \frac{( 2 x - 3 )}{6} d x

\frac{29}{9}

Decimal Notation

3.22222 \dots

Solution steps

\int_{2}^{4} x \frac{2 x - 3}{6} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{6} \cdot \int_{2}^{4} x (2 x - 3) d x

Expand

x (2 x - 3) : 2 x^{2} - 3 x

= \frac{1}{6} \cdot \int_{2}^{4} 2 x^{2} - 3 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

= \frac{1}{6} (\int_{2}^{4} 2 x^{2} d x - \int_{2}^{4} 3 x d x)

\int_{2}^{4} 2 x^{2} d x = \frac{112}{3}

\int_{2}^{4} 3 x d x = 18

= \frac{1}{6} (\frac{112}{3} - 18)

Simplify

\frac{1}{6} (\frac{112}{3} - 18) : \frac{29}{9}

= \frac{29}{9}

n = 2 \sum \infty \frac{1}{n !}

\frac{d}{d x} (\frac{x - 46}{x - 46})

x^{9} arccos (x)

\int \frac{x}{e ^{3 x}} d x

\int ln (x) x^{- 3} d x

What is the integral from 2 to 4 of x((2x-3))/6 ?
The integral from 2 to 4 of x((2x-3))/6 is 29/9