What is the integral from-2 to-1 of 3/y ?

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

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integral from-2 to-1 of 3/y

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

- 3 ln (2)

Decimal Notation

- 2.07944 \dots

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{y} d y = ln (∣ y ∣)

= 3 [ln ∣ y ∣]_{- 2}^{- 1}

Compute the boundaries:

- ln (2)

= 3 (- ln (2))

Simplify

= - 3 ln (2)

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