What is the integral from 0 to 3 of (2x)/9 ?

The integral from 0 to 3 of (2x)/9 is 1

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integral from 0 to 3 of (2x)/9

\int_{0}^{3} \frac{2 x}{9} d x

1

Solution steps

\int_{0}^{3} \frac{2 x}{9} d x

Take the constant out:

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

= \frac{2}{9} \cdot \int_{0}^{3} x d x

Apply the Power Rule

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

= \frac{2}{9} [\frac{x ^{2}}{2}]_{0}^{3}

Compute the boundaries:

\frac{9}{2}

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

Simplify

= 1

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What is the integral from 0 to 3 of (2x)/9 ?
The integral from 0 to 3 of (2x)/9 is 1