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

The integral from 0 to 2 of (x/2)^2 is 2/3

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integral from 0 to 2 of (x/2)^2

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

\frac{2}{3}

Solution steps

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

Apply Integration By Parts

: [\frac{x ^{3}}{4} - \int \frac{x ^{2}}{2} d x]_{0}^{2}

= [\frac{x ^{3}}{4} - \int \frac{x ^{2}}{2} d x]_{0}^{2}

\int \frac{x ^{2}}{2} d x = \frac{x ^{3}}{6}

= [\frac{x ^{3}}{4} - \frac{x ^{3}}{6}]_{0}^{2}

Join

\frac{x ^{3}}{4} - \frac{x ^{3}}{6} : \frac{x ^{3}}{12}

= [\frac{x ^{3}}{12}]_{0}^{2}

Compute the boundaries:

\frac{2}{3}

= \frac{2}{3}

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