What is the integral from 0 to 1 of 4ln(3x) ?

The integral from 0 to 1 of 4ln(3x) is 4(ln(3)-1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 1 of 4ln(3x)

\int_{0}^{1} 4 ln (3 x) d x

4 (ln (3) - 1)

Decimal

0.39444 \dots

Solution steps

\int_{0}^{1} 4 ln (3 x) d x

Take the constant out:

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

= 4 \cdot \int_{0}^{1} ln (3 x) d x

Apply Integration By Parts

= 4 [x ln (3 x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= 4 [x ln (3 x) - x]_{0}^{1}

Compute the boundaries:

ln (3) - 1

= 4 (ln (3) - 1)

What is the integral from 0 to 1 of 4ln(3x) ?
The integral from 0 to 1 of 4ln(3x) is 4(ln(3)-1)