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

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

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

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

2

Solution steps

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

Simplify

xx : x^{2}

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

Apply the Power Rule

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

Compute the boundaries:

9

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

Simplify

= 2

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