What is the integral from 0 to 0.5 of 2/(x-4) ?

The integral from 0 to 0.5 of 2/(x-4) is -0.26706…

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integral from 0 to 0.5 of 2/(x-4)

\int_{0}^{0.5} \frac{2}{x - 4} d x

- 0.26706 \dots

Solution steps

\int_{0}^{0.5} \frac{2}{x - 4} d x

Take the constant out:

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

= 2 \cdot \int_{0}^{0.5} \frac{1}{x - 4} d x

Apply u-substitution

: \int_{- 4}^{- 3.5} \frac{1}{u} d u

= 2 \cdot \int_{- 4}^{- 3.5} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 [ln ∣ u ∣]_{- 4}^{- 3.5}

Compute the boundaries:

- 0.13353 \dots

= 2 (- 0.13353 \dots)

Simplify

= - 0.26706 \dots

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What is the integral from 0 to 0.5 of 2/(x-4) ?
The integral from 0 to 0.5 of 2/(x-4) is -0.26706…