What is the integral from 0 to 1 of-yln(y) ?

The integral from 0 to 1 of-yln(y) is 1/4

Popular >

integral from 0 to 1 of-yln(y)

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

\frac{1}{4}

Decimal

0.25

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

: [\frac{1}{2} y^{2} ln (y) - \int \frac{y}{2} d y]_{0}^{1}

= - [\frac{1}{2} y^{2} ln (y) - \int \frac{y}{2} d y]_{0}^{1}

\int \frac{y}{2} d y = \frac{y ^{2}}{4}

= - [\frac{1}{2} y^{2} ln (y) - \frac{y ^{2}}{4}]_{0}^{1}

Compute the boundaries:

- \frac{1}{4}

= - (- \frac{1}{4})

Simplify

= \frac{1}{4}

\int_{3}^{7} 15 ln (x + 5) d x

\int_{1}^{2} 2 x - 2 d x

\int_{0}^{\frac{x}{2}} f (cos (x)) d x

\int_{1}^{e} \frac{1 + x + x ^{3}}{x} d x

\int_{1}^{3} (\frac{5}{x} - e^{- x}) d x

What is the integral from 0 to 1 of-yln(y) ?
The integral from 0 to 1 of-yln(y) is 1/4