What is the integral from 0 to 1 of (12ln(x)) ?

The integral from 0 to 1 of (12ln(x)) is -12

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integral from 0 to 1 of (12ln(x))

\int_{0}^{1} (12 ln (x)) d x

- 12

Solution steps

\int_{0}^{1} 12 ln (x) d x

Take the constant out:

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

= 12 \cdot \int_{0}^{1} ln (x) d x

Apply Integration By Parts

= 12 [x ln (x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= 12 [x ln (x) - x]_{0}^{1}

Compute the boundaries:

- 1

= 12 (- 1)

Simplify

= - 12

What is the integral from 0 to 1 of (12ln(x)) ?
The integral from 0 to 1 of (12ln(x)) is -12