What is the integral from 0 to 4 of x/3 ?

The integral from 0 to 4 of x/3 is 8/3

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integral from 0 to 4 of x/3

\int_{0}^{4} \frac{x}{3} d x

\frac{8}{3}

Decimal

2.66666 \dots

Solution steps

\int_{0}^{4} \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}^{4} x d x

Apply the Power Rule

= \frac{1}{3} [\frac{x ^{2}}{2}]_{0}^{4}

Compute the boundaries:

8

= \frac{1}{3} \cdot 8

Simplify

= \frac{8}{3}

What is the integral from 0 to 4 of x/3 ?
The integral from 0 to 4 of x/3 is 8/3