What is the integral from 1/2 to 4 of 1/(2x) ?

The integral from 1/2 to 4 of 1/(2x) is 3/2 ln(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1/2 to 4 of 1/(2x)

\int_{\frac{1}{2}}^{4} \frac{1}{2 x} d x

\frac{3}{2} ln (2)

Decimal Notation

1.03972 \dots

Solution steps

\int_{\frac{1}{2}}^{4} \frac{1}{2 x} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int_{\frac{1}{2}}^{4} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{2} [ln ∣ x ∣]_{\frac{1}{2}}^{4}

Compute the boundaries:

3 ln (2)

= \frac{1}{2} \cdot 3 ln (2)

Simplify

= \frac{3}{2} ln (2)

\int_{0}^{\frac{π}{2}} sec (θ) d θ

\int_{0}^{π} 3 x cos (3 x) d x

\int_{1}^{\infty} \frac{1}{2 x + 1} d x

\int_{3}^{2} sin (x) d x

\int_{0}^{2 π} cos^{2} (3 x) d x

What is the integral from 1/2 to 4 of 1/(2x) ?
The integral from 1/2 to 4 of 1/(2x) is 3/2 ln(2)