What is the integral from 0 to 8 of x(1/8 x) ?

The integral from 0 to 8 of x(1/8 x) is 64/3

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integral from 0 to 8 of x(1/8 x)

\int_{0}^{8} x (\frac{1}{8} x) d x

\frac{64}{3}

Decimal Notation

21.33333 \dots

Solution steps

\int_{0}^{8} x \frac{1}{8} x 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} xx d x

Simplify

xx : x^{2}

= \frac{1}{8} \cdot \int_{0}^{8} x^{2} d x

Apply the Power Rule

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

= \frac{1}{8} [\frac{x ^{3}}{3}]_{0}^{8}

Compute the boundaries:

\frac{512}{3}

= \frac{1}{8} \cdot \frac{512}{3}

Simplify

= \frac{64}{3}

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What is the integral from 0 to 8 of x(1/8 x) ?
The integral from 0 to 8 of x(1/8 x) is 64/3