What is the integral from 0 to 3 of (8x)/3 ?

The integral from 0 to 3 of (8x)/3 is 12

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integral from 0 to 3 of (8x)/3

\int_{0}^{3} \frac{8 x}{3} d x

12

Solution steps

\int_{0}^{3} \frac{8 x}{3} d x

Take the constant out:

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

= \frac{8}{3} \cdot \int_{0}^{3} x d x

Apply the Power Rule

= \frac{8}{3} [\frac{x ^{2}}{2}]_{0}^{3}

Compute the boundaries:

\frac{9}{2}

= \frac{8}{3} \cdot \frac{9}{2}

Simplify

= 12

What is the integral from 0 to 3 of (8x)/3 ?
The integral from 0 to 3 of (8x)/3 is 12