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

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

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

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

ln (2)

Decimal Notation

0.69314 \dots

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{t} d t = ln (∣ t ∣)

= \frac{1}{2} [ln ∣ t ∣]_{1}^{4}

Compute the boundaries:

2 ln (2)

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

Simplify

= ln (2)

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