What is the integral from 4 to 10 of 1/(x-2) ?

The integral from 4 to 10 of 1/(x-2) is 2ln(2)

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integral from 4 to 10 of 1/(x-2)

\int_{4}^{10} \frac{1}{x - 2} d x

2 ln (2)

Decimal

1.38629 \dots

Solution steps

\int_{4}^{10} \frac{1}{x - 2} d x

Apply u-substitution

= \int_{2}^{8} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{2}^{8}

Compute the boundaries:

2 ln (2)

= 2 ln (2)

What is the integral from 4 to 10 of 1/(x-2) ?
The integral from 4 to 10 of 1/(x-2) is 2ln(2)