What is the integral from 4 to 6 of xln(x/6) ?

The integral from 4 to 6 of xln(x/6) is -8ln(2/3)-5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 4 to 6 of xln(x/6)

\int_{4}^{6} x ln (\frac{x}{6}) d x

- 8 ln (\frac{2}{3}) - 5

Decimal Notation

- 1.75627 \dots

Solution steps

\int_{4}^{6} x ln (\frac{x}{6}) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (\frac{x}{6}) - \int \frac{x}{2} d x]_{4}^{6}

= [\frac{1}{2} x^{2} ln (\frac{x}{6}) - \int \frac{x}{2} d x]_{4}^{6}

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= [\frac{1}{2} x^{2} ln (\frac{x}{6}) - \frac{x ^{2}}{4}]_{4}^{6}

Compute the boundaries:

- 8 ln (\frac{2}{3}) - 5

= - 8 ln (\frac{2}{3}) - 5

\int_{2}^{- 2} x^{2} - 4 d x

\int_{- 1}^{0} - x^{3} d x

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

\int_{- 2}^{2} (11 - ∣ x ∣^{3}) d x

What is the integral from 4 to 6 of xln(x/6) ?
The integral from 4 to 6 of xln(x/6) is -8ln(2/3)-5