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

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

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integral from 0 to 1 of yln(y)

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

- \frac{1}{4}

Decimal Notation

- 0.25

Solution steps

\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}

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