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

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

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integral from 0 to 4 of x*x/8

\int_{0}^{4} x \cdot \frac{x}{8} d x

\frac{8}{3}

Decimal

2.66666 \dots

Solution steps

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

Simplify

xx : x^{2}

= \frac{1}{8} \cdot \int_{0}^{4} x^{2} d x

Apply the Power Rule

= \frac{1}{8} [\frac{x ^{3}}{3}]_{0}^{4}

Compute the boundaries:

\frac{64}{3}

= \frac{1}{8} \cdot \frac{64}{3}

Simplify

= \frac{8}{3}

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