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

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

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integral from 1 to 2 of 1/(3x)

\int_{1}^{2} \frac{1}{3 x} d x

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

Decimal

0.23104 \dots

Solution steps

\int_{1}^{2} \frac{1}{3 x} d x

Take the constant out:

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

= \frac{1}{3} \cdot \int_{1}^{2} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{3} [ln ∣ x ∣]_{1}^{2}

Compute the boundaries:

ln (2)

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

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