What is the integral from 6 to 12 of (36)/x ?

The integral from 6 to 12 of (36)/x is 36ln(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 6 to 12 of (36)/x

\int_{6}^{12} \frac{36}{x} d x

36 ln (2)

Solution steps

\int_{6}^{12} \frac{36}{x} d x

Take the constant out:

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

= 36 \cdot \int_{6}^{12} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 36 [ln ∣ x ∣]_{6}^{12}

Compute the boundaries:

ln (12) - ln (6)

= 36 (ln (12) - ln (6))

Simplify

= 36 ln (2)

\int_{- 1}^{2} (5 - 2 x) d x

\int_{0}^{1} 5 x + 7 d x

\int_{- 1}^{4} (- x^{2} + 3 x + 4) d x

\int_{\frac{1}{2}}^{1} \frac{1}{x ln ( x )} d x

\int_{0}^{\frac{π}{3}} (sin (3 x)) d x

What is the integral from 6 to 12 of (36)/x ?
The integral from 6 to 12 of (36)/x is 36ln(2)