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

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

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

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

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

Decimal

- 0.73240 \dots

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{2}{3} [ln ∣ x ∣]_{- 3}^{- 1}

Compute the boundaries:

- ln (3)

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

Simplify

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

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