What is the integral from 2 to 3.8 of ln(5-x) ?

The integral from 2 to 3.8 of ln(5-x) is 1.27705…

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integral from 2 to 3.8 of ln(5-x)

\int_{2}^{3.8} ln (5 - x) d x

1.27705 \dots

Solution steps

\int_{2}^{3.8} ln (5 - x) d x

Apply u-substitution

: \int_{3}^{1.2} - ln (u) d u

= \int_{3}^{1.2} - ln (u) d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{1.2}^{3} - ln (u) d u

Take the constant out:

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

= - (- \int_{1.2}^{3} ln (u) d u)

Apply Integration By Parts

: [u ln (u) - \int 1 d u]_{1.2}^{3}

= - (- [u ln (u) - \int 1 d u]_{1.2}^{3})

\int 1 d u = u

= - (- [u ln (u) - u]_{1.2}^{3})

Simplify

= [u ln (u) - u]_{1.2}^{3}

Compute the boundaries:

1.27705 \dots

= 1.27705 \dots

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What is the integral from 2 to 3.8 of ln(5-x) ?
The integral from 2 to 3.8 of ln(5-x) is 1.27705…