What is the integral from 2 to 3 of-ln(x-2) ?

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

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integral from 2 to 3 of-ln(x-2)

\int_{2}^{3} - ln (x - 2) d x

1

Solution steps

\int_{2}^{3} - ln (x - 2) d x

Take the constant out:

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

= - \int_{2}^{3} ln (x - 2) d x

Apply u-substitution

= - \int_{0}^{1} ln (u) d u

Apply Integration By Parts

= - [u ln (u) - \int 1 d u]_{0}^{1}

\int 1 d u = u

= - [u ln (u) - u]_{0}^{1}

Compute the boundaries:

- 1

= - (- 1)

Simplify

= 1

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