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

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

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

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

\frac{1}{2} (ln (2) - ln ∣ y ∣)

Solution steps

\int_{y}^{2} \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_{y}^{2} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{2} [ln ∣ x ∣]_{y}^{2}

Compute the boundaries:

ln (2) - ln ∣ y ∣

= \frac{1}{2} (ln (2) - ln ∣ y ∣)

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