What is the integral from 0 to 4 of (y^2)/4 ?

The integral from 0 to 4 of (y^2)/4 is 16/3

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integral from 0 to 4 of (y^2)/4

\int_{0}^{4} \frac{y ^{2}}{4} d y

\frac{16}{3}

Decimal

5.33333 \dots

Solution steps

\int_{0}^{4} \frac{y ^{2}}{4} d y

Take the constant out:

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

= \frac{1}{4} \cdot \int_{0}^{4} y^{2} d y

Apply the Power Rule

: [\frac{y ^{3}}{3}]_{0}^{4}

= \frac{1}{4} [\frac{y ^{3}}{3}]_{0}^{4}

Compute the boundaries:

\frac{64}{3}

= \frac{1}{4} \cdot \frac{64}{3}

Simplify

= \frac{16}{3}

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What is the integral from 0 to 4 of (y^2)/4 ?
The integral from 0 to 4 of (y^2)/4 is 16/3