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

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

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integral from 0 to 1 of-ln(x)

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

1

Solution steps

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

Take the constant out:

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

= - \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

\frac{d y}{d x} = - y (x + 1)

x + 4 x + 2

x \to 3 lim \frac{\frac{1}{3} x - \frac{1}{3}}{x - 3}

8 cos (x)

2 t + 1

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