What is the integral from 0 to 3 of 1/3 x ?

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

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integral from 0 to 3 of 1/3 x

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

\frac{3}{2}

Decimal

1.5

Solution steps

\int_{0}^{3} \frac{1}{3} x 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{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}

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