What is the integral from 0 to 3 of x/3 ?

The integral from 0 to 3 of x/3 is 3/2

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integral from 0 to 3 of x/3

\int_{0}^{3} \frac{x}{3} d x

\frac{3}{2}

Solution steps

\int_{0}^{3} \frac{x}{3} d x

Take the constant out:

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

= \frac{1}{3} \cdot \int_{0}^{3} x d x

Apply the Power Rule

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

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

Compute the boundaries:

\frac{9}{2}

= \frac{1}{3} \cdot \frac{9}{2}

Simplify

= \frac{3}{2}

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