What is the integral from 0 to 1 of 4ln(x) ?

The integral from 0 to 1 of 4ln(x) is -4

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integral from 0 to 1 of 4ln(x)

\int_{0}^{1} 4 ln (x) d x

- 4

Solution steps

\int_{0}^{1} 4 ln (x) d x

Take the constant out:

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

= 4 \cdot \int_{0}^{1} ln (x) d x

Apply Integration By Parts

= 4 [x ln (x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= 4 [x ln (x) - x]_{0}^{1}

Compute the boundaries:

- 1

= 4 (- 1)

Simplify

= - 4

What is the integral from 0 to 1 of 4ln(x) ?
The integral from 0 to 1 of 4ln(x) is -4