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

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

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integral from 0 to 8 of x/8

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

4

Solution steps

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

Take the constant out:

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

= \frac{1}{8} \cdot \int_{0}^{8} x d x

Apply the Power Rule

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

= \frac{1}{8} [\frac{x ^{2}}{2}]_{0}^{8}

Compute the boundaries:

32

= \frac{1}{8} \cdot 32

Simplify

= 4

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