What is the integral from 0 to 1 of (y^2)/2 ?

The integral from 0 to 1 of (y^2)/2 is 1/6

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integral from 0 to 1 of (y^2)/2

\int_{0}^{1} \frac{y ^{2}}{2} d y

\frac{1}{6}

Decimal Notation

0.16666 \dots

Solution steps

\int_{0}^{1} \frac{y ^{2}}{2} d y

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{1} y^{2} d y

Apply the Power Rule

: [\frac{y ^{3}}{3}]_{0}^{1}

= \frac{1}{2} [\frac{y ^{3}}{3}]_{0}^{1}

Compute the boundaries:

\frac{1}{3}

= \frac{1}{2} \cdot \frac{1}{3}

Simplify

= \frac{1}{6}

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What is the integral from 0 to 1 of (y^2)/2 ?
The integral from 0 to 1 of (y^2)/2 is 1/6