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

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

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integral from 1 to 0 of ln(x)

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

1

Solution steps

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

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

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

Apply Integration By Parts

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

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

\int 1 d x = x

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

Compute the boundaries:

- 1

= - (- 1)

Simplify

= 1

\int_{1}^{4} \frac{1}{( x - 2 ) ^{\frac{3}{2}}} d x

\int_{0}^{1} x \cdot x d x

\int_{1}^{4} \frac{1}{( x + 3 ) ^{2}} d x

\int_{- 3}^{3} \frac{1}{x - 1} d x

\int_{2}^{3} (2 + 2 y)^{2} d y

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